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.

Erik Lamela doubled the hosts' lead 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 on 25 January.

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 saved by Mejias.

He should have also been put through on goal, but team-mate Moura instead opted to shoot instead 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 it 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."

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."