Harry Redknapp's side were on the verge of moving within four points of leaders Manchester City after Rafael van der Vaart opened the scoring on the stroke of half-time.
Swansea had not managed to pick up a single point this season after conceding the first goal, but they bucked that trend as a period of heavy pressure was rewarded when Sinclair netted his fifth goal of the campaign with just six minutes remaining.
Tottenham had lost just once in the league since the end of August but this result will have felt like a defeat, especially in the wake of Manchester United's shock defeat to Blackburn earlier in the day.
Redknapp's men are now six points behind City and United and that gap will increase to nine if the leaders beat Sunderland on Sunday.
Nathan Dyer almost gave Swansea a dream start inside four minutes after Mark Gower had dispossessed Scott Parker, but his curling effort was palmed away by Brad Friedel.
Spurs responded and Croatian midfielder Luka Modric fizzed an effort narrowly wide of Michel Vorm's right-hand post after 14 minutes.
The north Londoners should have led after 32 minutes after a horrible pass from Dyer played Emmanuel Adebayor in on goal, but Vorm added to his growing reputation with a superbly timed sliding challenge to take the ball away from the Togolese forward.
The pressure finally told when they took the lead just a minute before the break as Benoit Assou-Ekotto's cross was turned back into danger by Joe Allen and turned home by Van der Vaart.
Tottenham almost doubled their lead 60 seconds after half-time as Younes Kaboul was given far too much room to advance, the centre-half being denied by Vorm after a neat exchange with Adebayor.
Swansea were looking vulnerable to Tottenham's rapid counter-attacks and a misjudged Allen pass allowed Adebayor to tee up Van der Vaart, only for Vorm to make the block low to his right.
Bale prodded just wide as Swansea struggled to contain the seamless movement of the likes of Modric, Van der Vaart and Sandro.
Spurs skipper Parker limped off with an injury, while Swansea introduced top scorer Danny Graham from the bench and the pattern of the game suddenly changed.
Graham diverted a fierce Sinclair drive over the bar and it took a fantastic clearance from Kyle Walker to deny the striker a tap-in as Stephen Dobbie stabbed the ball across the box.
Modric blocked a Sinclair effort as Swansea piled forward and the hosts finally equalised in the 84th minute.
Angel Rangel's ball into the box deflected off Benoit Assou-Ekotto and as Friedel hesitated the ball broke loose for Sinclair to fire home from close range.
Source: AFP
Source: AFP