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Swansea striker Bafetimbi Gomis needed several minutes of treatment on the pitch after collapsing during his side's defeat at Tottenham.
Gomis was carried off, having collapsed after Nacer Chadli put Spurs 1-0 up, but Swansea later said he was "fine".
Swansea equalised through Ki Sung-yeung soon after play restarted.
Ryan Mason's first league goal restored Spurs' lead in the second half and Andros Townsend made it 3-1 before Gylfi Sigurdsson set up a tense finish.
Tottenham paid tribute to Double-winning captain Dave Mackay, who died on Tuesday at the age of 80, with a minute's applause before kick-off.
And Spurs did justice to one of their greatest players with an impressive performance which got their challenge for a top-four place back on track with a first Premier League victory since beating Arsenal on 7 February.
It helped them get over the disappointment of losing Sunday's League Cup final to Chelsea and going out of the Europa League to Fiorentina at the last-16 stage last week.
The result prevented Swansea recording a third successive win and continued their terrible record at White Hart Lane where they have never won a league game in 16 attempts.
Garry Monk's side is chasing a highest ever Premier League point tally of 47 but were badly hindered by losing Gomis in worrying circumstances.
Chadli had just volleyed Tottenham ahead after seven minutes from Danny Rose's fine cross when the striker, 29, collapsed.
The France international has a history of fainting and received oxygen and four minutes of attention before going off on a stretcher in a conscious state.
A number of players were visibly upset but despite seeing their attacking strength greatly depleted Swansea equalised after 19 minutes.
A free-kick from former Tottenham midfielder Sigurdsson came back off the post and after Spurs failed to clear, Neil Taylor played in Ki to slip the ball through the legs of Hugo Lloris from a tight angle.
The Swans started the second half impressively with Jonjo Shelvey forcing Lloris into a save with a long-range effort before Tottenham took control.
Mason, 23, continued his impressive season when he burst into the box following a strong run from Christian Eriksen to thump a right-footed shot past Lukasz Fabianski and put Tottenham back in front.
When England international Townsend then capped a swift counter-attack with a superb solo effort, cutting in to slot home his seventh goal of the season, with half-an-hour to go, Mauricio Pochettino's side looked set to go on and add to their tally.
But Swansea hit back late on with Sigurdsson volleying home his 11th goal of the season with a minute to go.
And it took an outstanding save from Lloris in injury time to keep out a header from Federico Fernandez to prevent the visitors from taking their first point at Tottenham since 1930.
Tottenham manager Mauricio Pochettino:
"I'm happy for the players because they deserve this victory. It was a very important three points for us, I'm happy for the performance, it was fantastic.
"It was 3-2 but we shoot many times and had more than 60 per cent possession - only in the last minute did we put risk in the game.
"We were lucky to have a big save from Hugo - one of the best 'keepers in world."
Swansea boss Garry Monk: In the first half we played really well. Had a few chances and there were a couple of close offside decisions, which, had they gone our way, we would have had further chances to score.
"In the second half we conceded two goals following mistakes, which set us back a bit. But we got that late goal and nearly scored an equaliser. That's how quickly things can change in football."
