Tottenham moved back to within two points of Premier League leaders Leicester after battling back from behind to beat a dogged Swansea side.
Alberto Paloschi gave the visitors the lead after Angel Rangel's shot fell to him via team-mate Jack Cork.
Swansea goalkeeper Lukasz Fabianski made a series of superb saves, before Nacer Chadli deflected in Kyle Walker's shot to equalise with 20 minutes left.
Danny Rose then drove in the winner after Swansea failed to clear a corner.
Hopes have been growing at White Hart Lane of a first league title since 1961, but the pressure was on to beat struggling Swansea after Leicester opened up a five-point lead with a victory over Norwich on Saturday.
Mauricio Pochettino's side were utterly dominant - managing 34 shots at goal to Swansea's 10 - but were frustrated by determined defending and brilliant goalkeeping.
Spurs could have forgiven for thinking it was not going to be their day, particularly when the outstanding Fabianski dived acrobatically to his right to claw out Christian Eriksen's free-kick early in the second half.
Fabianski had earlier made an excellent stop to deny Harry Kane from close range, but was finally beaten as substitute Chadli struck and Rose added his first goal of the season.
For Pochettino, it was a sign that his players have the character to force victories when fortune appears to be against them.
Pochettino's side secured a sixth successive league victory to keep the pressure on Leicester - on a day when neighbours Arsenal lost ground with a defeat at Manchester United.
The concern for Tottenham's manager is that his key players steer clear of injury as the attempt to juggle domestic demands with the Europa League.
England forward Kane was patched up to play in a face mask after missing Thursday's victory over Fiorentina with a broken nose.
There was concern too before kick-off as midfielder Dele Alli, an inspirational figure for them this season, turned his ankle in the warm-up.
Alli was able to play the full game, but did not look at his best. Pochettino must hope that the midfielder is in better shape for Wednesday's trip to West Ham.
Francesco Guidolin will have been cheered with the spirit his side showed - which was just the pick-me-up that the Swansea manager needed as he battles a chest infection.
His side showed attacking guile on their occasional breaks forward, while Paloschi took his goal smartly to score for the first time since his move from Chievo in January.
That came after Tottenham keeper Hugo Lloris made a superb early save to tip over Gylfi Sigurdsson's shot from six yards, and the France international was alert too late in the game to beat out another Paloschi shot.
Guidolin, though will feel a sense of frustration that his team were unable to get anything from the game after leading with 20 minutes left.
It means that, after four league games without victory, Swansea remain only three points above the relegation zone. Matches against Norwich, Bournemouth and Aston Villa in March will go a long way towards deciding their fate.
Tottenham head coach Mauricio Pochettino: "Fabianski was great. He was man of the match. Sometimes football is difficult. You play well but find it hard to score. The good thing is that the team fight. It is a fantastic win.
"Our mentality is to look to the next game and go step by step. Now we need to focus again. We have a strong squad and we will try to manage it in the right way."
