The Tottenham manager, Harry Redknapp, remained defiant over his side's hopes of claiming the Premier League title despite dropping two points late on.
The Londoners wasted a chance to trim the gap on the Manchester duo at the Premier League summit following Scott Sinclair's late equaliser.
Redknapp's contenders arrived in south Wales buoyed by Blackburn Rovers' shock win at rivals Manchester United in the early kick-off, and took a 44th-minute lead through Rafael van der Vaart.
The Tottenham left-back Benoît Assou-Ekotto saw his low cross diverted by Joe Allen into the path of Van der Vaart whose left-footed shot deflected off Ashley Williams into the bottom corner. But the flying winger Sinclair gained a vital point for Swansea on 84 minutes after an error by the Tottenham goalkeeper Brad Friedel. Angel Rangel surged down the right and, after Friedel failed to gather the Spanish full-back's centre, Sinclair tapped home for his fifth goal of the season.
Redknapp said: "We are disappointed to be a goal ahead and then get pegged back. It was a sloppy goal to concede. One or two of the players switched off and it was a catalogue of errors. But not many teams will come here and pick up three points. We were hanging on in the final 20 minutes.
"The way Brendan Rodgers has got his players playing is incredible and only Manchester United have done that this season so give credit to them. There is a long way to go. It's so difficult to win football matches. Who could have seen Blackburn winning at United and Villa at Chelsea? You aren't going to win every game and we don't have the divine right to do so. We just have to keep going."
Tottenham arrived as the form team in the Premier League following a rewarding run yielding just one loss in 15 matches.
Yet the Swansea manager Rodgers, who made six changes from the draw against Queens Park Rangers as a result of the festive fixture scheduling which he slammed as "ridiculous", would have been the happier manager after a bright opening.
Nathan Dyer tested Friedel with a left-footed curler and Sinclair, after escaping the attention of marker Scott Parker, miscued Mark Gower's intelligent corner before Luka Modric managed to produce the visitors' first attempt on goal in the 13th minute. Swansea, despite the vast difference in resources and experience at this level, continued to probe, and almost took a surprise lead through Sinclair.
Luke Moore, one of Rodgers' changes, was handed time and space and his cut-back intended for Stephen Dobbie found Sinclair 25 yards from goal.
The winger came in off the left flank and beat Friedel with an arcing shot, but his effort flew just inches over the crossbar.
Then Swansea almost pressed the self-destruct button on 33 minutes when Emmanuel Adebayor came close to seizing on Dyer's poor back-pass, but Michel Vorm averted the danger.
Gareth Bale was unusually quiet and received a yellow card from referee Phil Dowd for a blatant dive. But, moments later, Spurs bagged the opener as Van der Vaart slammed the ball past countryman Vorm from six yards for his seventh goal of the season.
The omens did not look good for Swansea as the Welsh side have yet to come from behind in the top-flight all season. Tottenham continued on top in the second period as Younès Kaboul was denied by Vorm at his near post following a neat one-two with Adebayor.
The Togo striker also provided Van der Vaart with the chance to double the visitors' advantage, but Vorm dived low to his right to turn his curling effort around the post.
Swansea rallied in search of an equaliser as Moore's shot was deflected by William Gallas before the half-time substitute Rangel shaved the post with a volley from Dobbie's resulting corner.
Rodgers threw on striker Danny Graham and the club-record signing almost came up trumps with a flicked header on 75 minutes. Sinclair had a shot cleared off the line in the 82nd minute by Modric before the wideman equalised two minutes later from close-range.
"I'm really proud of the players' performance and I felt it was the least we deserved," said Rodgers. "Tottenham are the form team in the country and are real title contenders, but I thought we were brilliant. It was a magnificent performance. We were unfortunate to go behind as the cross took a deflection. It was harsh on us. I said to the players at half-time, I don't want to be heroic losers.
"But we kept going and showed the development in the group. We pressed from the first whistle and thoroughly deserved the point. We are really buoyed and the performance will give us great confidence moving forward."
Swansea (4-3-3): Vorm; Richards (Rangel, h-t), Monk, Williams, Taylor; Gower (Agustien, 62), Allen, Dobbie; Dyer, Moore (Graham, 69), Sinclair.
Tottenham (4-5-1): Friedel; Walker, Gallas, Kaboul, Assou-Ekotto; Van der Vaart (Defoe, 71), Sandro, Parker (Livermore, 72), Modric, Bale; Adebayor.
Referee Phil Dowd.
Man of the match Williams (Swansea).
Match rating 8/10.