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 equalized 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 defense 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.
TWEET OF THE MATCH
Chris Wathan @ChrisWathan – "'Harry Kane he's one of our own' chant Swansea fans"
'Harry Kane he's one of our own' chant Swansea fans
— Chris Wathan (@ChrisWathan) October 4, 2015
Lukasz Fabianski 6 (out of 10)
Angel Rangel: 6
Ashley Williams: 7
Federico Fernandez: 7
Neil Taylor: 6
Ki Sung-yueng: 6
Jonjo Shelvey: 6
Jefferson Montero: 7
Andre Ayew: 7
Gylfi Sigurdsson: 6
Bafetimbi Gomis: 6
Modou Barrow (on for Sigurdsson, 74mins): 6
Jack Cork (on for Shelvey, 86mins) 6
Hugo Lloris: 6
Kyle Walker: 6
Toby Alderweireld: 7
Jan Vertonghen: 7
Ben Davies: 7
Eric Dier: 7
Dele Alli: 7
Nacer Chadli: 7
Christian Eriksen: 8
Erik Lamela: 6
Harry Kane: 6
Andros Townsend (on for Lamela, 57mins): 6
Clinton N'Jie: (on for Chadli, 64mins) 6
Mousa Dembele (on for Kane, 81mins) 6
Christian Eriksen: The Dane's dead-ball ability is a delight to behold. Two free-kicks – the second one a stunner – secured a deserved point for Tottenham.
MOMENT OF THE MATCH
Harry Kane's volleyed own goal was a contender, if only for its comedy value. But Eriksen's second free-kick was right out of the top drawer, giving Lukasz Fabianski absolutely no chance in the Swansea goal. Probably not a better dead-ball expert in the Premier League right now.
VIEW FROM THE BENCH
Swansea manager Garry Monk recalled Jefferson Montero and the Ecuador winger, involved in a fascinating battle with Kyle Walker, gave the hosts penetration down the right flank. Spurs boss Mauricio Pochettino had made only two changes from Thursday's game at Monaco but his players showed little effect of that Europa League excursion and produced another excellent performance to keep their unbeaten run going.
MOAN OF THE MATCH
Hard to be picky in what was an excellent encounter. But had Tottenham showed a greater composure in front of goal they would surely have taken all three points. The shame for them was that Harry Kane showed a clinical touch in front of his own goal.
WHO'S UP NEXT?
Swansea v Stoke (Premier League, October 19)
Tottenham v Liverpool (Premier League, October 17)
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