Christian Eriksen stunned Swansea with two brilliant free-kicks after Tottenham striker Harry Kane had scored a spectacular own goal.
Eriksen scored an 89th-minute winner on his previous visit to the Liberty Stadium and his dead-ball accuracy spared Spurs' blushes in a thrilling 2-2 Barclays Premier League draw.
Tottenham dominated for long periods but could not take their chances in open play and secure what would have been a fourth straight league win for the first time since January 2014.
Twice, they had to come from behind after Andre Ayew's header and then a horrible Kane mistake had handed Swansea the lead.
England striker Kane has only scored once for Spurs this season, in last week's 4-1 victory over league leaders Manchester City, but he found his own net when he miscued Jonjo Shelvey's corner after 31 minutes.
Spurs started on the front foot as Swansea struggled to cope with their high pressing tactics and the hosts almost paid the price for giving the ball away in dangerous areas.
Bafetimbi Gomis' careless touch from a throw allowed Nacer Chadli to take aim from 25 yards but Lukasz Fabianski comfortably collected.
Swansea had hardly broken out of their own half when they launched a stunning length-of-the-field move which ended with their first goal in open play for 310 minutes.
Fabianski started in his own area and Federico Fernandez, Angel Rangel, Gomis and Gylfi Sigurdsson were all involved before Jefferson Montero crossed for Ayew to head home his fourth Swansea goal.
Spurs responded by Chadli forcing a good save from Fabianski at his near-post but the Poland goalkeeper had no answer to Eriksen's 27th-minute free-kick which went over the wall and left him badly wrong-footed.
Eriksen almost gave Spurs the lead moments later but the visitors were stunned when Kane put through his own net.
Under Mauriccio Pochettino, however, Spurs have developed a resilient streak and they showed it again as they finished half on top with Eriksen their beating creative heart.
The Dane almost equalised with a carbon-copy of his successful free-kick, but Fabianski this time managed to paw the ball away.
And Fabianski produced an even better save four minutes before the break when the Swansea defence stood off Eriksen and he tipped a well-struck low shot around the post.
Spurs were probably cursing their luck at the break and Kane almost brought them level within seconds of the re-start.
But Swansea were showing signs of improvement and Montero and Ayew were finding more space down the flanks, the former crossing for Gomis to head over.
The French striker failed to find the target again when Sigurdsson met a half-cleared corner on the volley and, with the ball coming at him at high speed, Gomis put it wide.
Swansea were on top for the first time but they were punished in spectacular style when Shelvey pushed Dele Alli over on the edge of the box and Eriksen sent the free-kick into the top corner.
Eriksen's equalizer galvanized Spurs and they finished the stronger with Alli and substitute Andros Townsend forcing fine stops from Fabianski, but Swansea almost snatched it at the death with Hugo Lloris pushing Fernandez's header onto the crossbar.
