Match ends, Tottenham Hotspur 2, Middlesbrough 1.
Tottenham gained a hard-fought victory over Championship side Middlesbrough in their FA Cup third-round replay.
Spurs were gifted a second-minute lead when Boro goalkeeper Tomas Mejias passed the ball to Giovani lo Celso, who cut inside a challenge and scored.
Lamela doubled the hosts’ advantage after 15 minutes when he flicked the ball past Mejias after a fine run.
George Saville pulled one back late on for Boro with a low strike from 20 yards out, but it was not enough.
Middlesbrough substitute Rudy Gestede had a chance to force extra-time but he could only head over the bar from eight yards as Spurs held on for the win.
Tottenham, who have won the FA Cup eight times, will play at Southampton in the fourth round later this month.
The FA Cup represents Tottenham’s best chance of a trophy this season; they are eighth in the Premier League, out of the EFL Cup – after a shock third-round exit on penalties at League Two Colchester – and have a tricky tie against Bundesliga leaders RB Leipzig in the Champions League last 16.
If they were to win the FA Cup, it would be their first trophy since lifting the League Cup in 2008.
Boro boss Jonathan Woodgate scored the winner for Spurs in that Wembley final against Chelsea 12 years ago, as part of a team that also included his assistant boss Robbie Keane.
Woodgate and Keane’s current side, cheered on by 3,700 fans who had travelled down from the north east in the first FA Cup tie at the new Tottenham Hotspur Stadium, made an awful start after a horrible error from Mejias.
The Spanish goalkeeper, who played under Jose Mourinho at Real Madrid in 2011, tried to play a ball to Marvin Johnson, but Lo Celso intercepted the pass inside the penalty area, cut inside a challenge and curled a low effort into the net.
Boro had a chance to equalise in the 13th minute but Lukas Nmecha, on loan from Manchester City, had his effort well saved by Paulo Gazzaniga and that proved costly as Lamela’s goal three minutes later doubled the hosts lead.
Woodgate would be again unhappy with his side’s defending as Jonny Howson was dispossessed 35 yards from goal, before Lamela was able to go on a jinking run and flick the ball with the outside of his foot past Mejias from 12 yards.
Spurs then wasted numerous chances to kill the match off as Lamela shot over on the turn, Ryan Sessegnon had an effort pushed wide, Japhet Tanganga shot just off target and Lucas Moura wasted a chance from a counter-attack.
Boro, 16th in the Championship had opportunities to get themselves back into the tie, but Paddy McNair shot well over when unmarked eight yards out and Lewis Wing’s direct free-kick was pushed around the post by Gazzaniga.
Saville’s 83rd-minute goal for the visitors gave them hope, but they could not find an equaliser.
With Harry Kane out until at least April after surgery on a hamstring injury, Spurs are light on attacking options and boss Mourinho took the chance to ease the workload on his other senior forwards, with Son Heung-min playing only the last 30 minutes, and Dele Alli making a brief appearance as a substitute, coming on after Saville’s goal.
That meant another appearance in the starting 11 for Christian Eriksen, despite the midfielder, out of contract at the end of season, being linked with a January move to Inter Milan.
Eriksen, who has been with Spurs since 2013, had a chance to score after flicking the ball over the head of an opponent and being fouled – driving the resulting free-kick low and seeing it saved by Mejias.
He should have also been put through on goal, but team-mate Moura instead opted to shoot instead as Spurs counter-attacked and could only drag an effort wide.
Eriksen nearly scored late in the second half when his low delivery in the penalty area was missed by everyone and Mejias had to get down well to push the ball away one-handed.
This was Tottenham’s 31st match of the season and their 14th in a 53-day period since Mourinho’s first game in charge on 23 November.
He will be pleased with the win and that extra-time was not needed but will be frustrated with the late goal conceded, meaning they have only kept one clean sheet in his 14 games in charge.
Tottenham boss Jose Mourinho, speaking to BBC Sport, said: “Three-nil was so close so many times. I told my players at half time if we don’t score [to make it] 3-0, then if went 2-1 we would be in trouble and it happened.
“We knew the opponents were hard. They brought on Gestede and went direct and made problems and when it was 2-1 we knew it was going to be difficult.
“We tried our best. The boys are trying their best. They dealt well with many set-piece situations. We did lots of things well. We conceded the goal, a bit frustrating, but more frustrating was that we did not score three, four or five.”
Asked if the FA Cup was the priority for Spurs now, Mourinho replied: “In this moment, it is not the priority. The priority is to play a difficult match against Watford in the Premier League. When Southampton comes, it will be the priority.”
Middlesbrough manager Jonathan Woodgate, speaking to BBC Sport, said: “I don’t like losing games and when you gift Tottenham goals like that so early, you’re fearing the worst. But my players showed character and we ran them close.
“If there’s a way to lose then it’s like that – putting a real show on and a real fight. The players gave everything for the shirt.”
On the early error from keeper Tomas Mejias, Woodgate added: “We all make mistakes and I won’t hammer anyone for that – we want them to play out from the back.”
Tottenham, who have only taken one point from their past three Premier League matches, return to league action on Saturday when they play at Watford (12:30 GMT), before a home game against Norwich on Wednesday, 22 January (19:30). The fourth-round FA Cup tie at Southampton will be played on Saturday, 25 January (15:00).
Middlesbrough play again in three days time with an away match in the Championship at Fulham on Friday (19:45 GMT), before entertaining Birmingham on 21 January (19:45).
Match ends, Tottenham Hotspur 2, Middlesbrough 1.
Second Half ends, Tottenham Hotspur 2, Middlesbrough 1.
Attempt blocked. Dele Alli (Tottenham Hotspur) right footed shot from the right side of the six yard box is blocked. Assisted by Son Heung-Min.
Attempt missed. Ashley Fletcher (Middlesbrough) header from the centre of the box misses to the right. Assisted by Marvin Johnson with a cross.
Attempt blocked. Erik Lamela (Tottenham Hotspur) left footed shot from the left side of the box is blocked. Assisted by Giovani Lo Celso.
Attempt missed. Christian Eriksen (Tottenham Hotspur) right footed shot from outside the box is too high from a direct free kick.
Son Heung-Min (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Jonny Howson (Middlesbrough).
Substitution, Tottenham Hotspur. Dele Alli replaces Eric Dier.
Attempt missed. Rudy Gestede (Middlesbrough) header from the centre of the box is too high. Assisted by Marvin Johnson with a cross following a corner.
Corner, Middlesbrough. Conceded by Harry Winks.
Attempt blocked. Jonny Howson (Middlesbrough) left footed shot from outside the box is blocked. Assisted by Marcus Tavernier.
Goal! Tottenham Hotspur 2, Middlesbrough 1. George Saville (Middlesbrough) right footed shot from outside the box to the bottom left corner. Assisted by Rudy Gestede with a headed pass.
Foul by Eric Dier (Tottenham Hotspur).
Dael Fry (Middlesbrough) wins a free kick in the defensive half.
Attempt missed. Rudy Gestede (Middlesbrough) header from the centre of the box is high and wide to the left. Assisted by Marvin Johnson with a cross.
Corner, Tottenham Hotspur. Conceded by George Saville.
Attempt blocked. Son Heung-Min (Tottenham Hotspur) left footed shot from outside the box is blocked. Assisted by Harry Winks.
Substitution, Middlesbrough. Rudy Gestede replaces Lukas Nmecha.
Corner, Middlesbrough. Conceded by Giovani Lo Celso.
Attempt blocked. George Saville (Middlesbrough) left footed shot from outside the box is blocked. Assisted by Marcus Tavernier.
Substitution, Middlesbrough. Marcus Tavernier replaces Djed Spence.
Japhet Tanganga (Tottenham Hotspur) wins a free kick on the right wing.
Foul by Marvin Johnson (Middlesbrough).
Corner, Tottenham Hotspur. Conceded by Dael Fry.
Attempt missed. Lukas Nmecha (Middlesbrough) header from the centre of the box is too high. Assisted by Marvin Johnson with a cross following a corner.
Corner, Middlesbrough. Conceded by Jan Vertonghen.
Erik Lamela (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Ashley Fletcher (Middlesbrough).
Attempt blocked. Giovani Lo Celso (Tottenham Hotspur) left footed shot from the centre of the box is blocked. Assisted by Christian Eriksen.
Corner, Tottenham Hotspur. Conceded by Adam Clayton.
Corner, Middlesbrough. Conceded by Eric Dier.
Foul by Japhet Tanganga (Tottenham Hotspur).
Marvin Johnson (Middlesbrough) wins a free kick on the left wing.
Attempt saved. Lukas Nmecha (Middlesbrough) right footed shot from a difficult angle on the right is saved in the bottom right corner. Assisted by Adam Clayton.
Foul by Son Heung-Min (Tottenham Hotspur).
Adam Clayton (Middlesbrough) wins a free kick in the defensive half.
Substitution, Tottenham Hotspur. Son Heung-Min replaces Lucas Moura.
Foul by Giovani Lo Celso (Tottenham Hotspur).
Djed Spence (Middlesbrough) wins a free kick in the defensive half.