Van der Vaart converted Benoit Assou-Ekotto's deflected left-wing cross.
But Sinclair levelled as he capitalised on a Brad Friedel error as the keeper failed to hold Angel Rangel's cross.
The Spurs stopper fumbled Rangel's teasing right-wing centre, which took a wicked deflection of Assou-Ekotto's boot, under pressure from Swans striker Danny Graham and Sinclair tapped into an empty net.
The close presence of his own defenders William Gallas and Younes Kaboul would not have helped Friedel's cause as the American made an uncharacteristic mistake.
Swansea v Tottenham fact-file
Tottenham have not won in Swansea since September 1946
Swansea have British football's tightest defensive home record
The Liberty Stadium has seen the fewest amount of goals in the Premier League this season with 16 goals scored
Tottenham finish the year as London's highest-placed team for the first time since 1995
Tottenham have lost just once in 16 Premier League games while Swansea have won one in nine
But Sinclair and Swansea boss Brendan Rodgers, who ran down the touch-line and punched the air to celebrate the goal, did not care as it was a much-needed point for a Swansea side that looked set to drop to within four points of the relegation zone.
On the balance of play, the hosts deserved their point. Sinclair had a shot cleared off the line by Spurs midfielder Luka Modric and Rangel and Luke Moore both went close as Swansea chased an equaliser.
Rodgers's men also restricted an in-form Spurs side to half chances and long-range efforts but Harry Redknapp will be disappointed as the visiting manager insisted his side needed a win at the Liberty Stadium if they had hopes of a first title since 1961.
Swansea are a pleasure to watch - Redknapp
Redknapp, already without defender Ledley King who has knee problems, will also be concerned by the loss of key midfielder Scott Parker after the England international was forced off injured with 20 minutes remaining, needing an ice pack on his right knee.
Jazz Richards suffered a torrid time at right-back with both Gareth Bale and Assou-Ekotto testing Swansea's inexperienced defender throughout.
And it was Cameroon's Assou-Ekotto who beat Richards before his cut-back was inadvertently knocked into Van der Vaart's path by Swansea midfielder Joe Allen leaving the Dutch forward to acrobatically volley in his eighth of the season, via a deflection off Ashley Williams.
Van der Vaart's first league goal for two months was only the fourth goal Swansea had conceded at home this season - and the fifth could have come just after half-time.
Rodgers happy with ending to 'iconic' year
The legs of Swansea keeper Michel Vorm kept out Kaboul's near-post strike after the Spurs centre-back's surging run from defence and Van der Vaart wasted a great chance to extend Tottenham's lead from Emmanuel Adebayor's defence-splitting pass but his tame first-time 25-yarder was routine for Vorm.
Spurs right-back Kyle Walker, with Sinclair waiting to pounce, was forced to make a goal-saving intervention from Stephen Dobbie's goal-bound shot soon after.
But Sinclair, the Swans' Championship play-off hero and top-scorer last season, was again the man as his fifth goal of the season earned the homes side a first point this term after going behind, a result that leaves Spurs six points adrift of the Manchester clubs in the title race.
Swansea manager Brendan Rodgers:
"This will be a really good result for us psychologically. I said to the players at half-time that we don't want to come off the field as heroic losers.
"People would be saying it's alright playing our tippy-tappy football but it's no good if you then lose the game, but it was a fantastic performance.
"It's always good to put on a performance and result against a top team and you can see our growth."
Tottenham manager Harry Redknapp:
"It was a sloppy goal. One or two of them switched off and we didn't pick up Sinclair, we have let him come in unmarked so it was a catalogue of errors, but that's how it goes.
"It was a tight game. They are a good side, I like the way they play. The way they pass is amazing really. The belief Brendan has installed into them to play is top class.
"Anyone coming here and winning will do well, only United have won here and that was a tough game.
"You are obviously disappointed when you are winning and get pegged back, but the last 20 minutes they came on strong and, in the end, deserved their equaliser."
Full Time The final whistle goes and the game is over.
Free kick awarded for an unfair challenge on Benoit Assou-Ekotto by Nathan Dyer. Direct free kick taken by Benoit Assou-Ekotto.
Emmanuel Adebayor takes a shot. Save by Michel Vorm.
Free kick awarded for an unfair challenge on Luka Modric by Joe Allen. Gareth Bale fires a strike on goal direct from the free kick.
Stephen Dobbie crosses the ball from the free kick right-footed from left wing.
Booking Jake Livermore goes into the book for unsporting behaviour.
Free kick awarded for a foul by Jake Livermore on Neil Taylor.
Assist by Angel Rangel.
83:32 Goal scored
Goal! - Scott Sinclair - Swansea 1 - 1 Tottenham Scott Sinclair gets on the score sheet with a goal from deep inside the penalty box low into the middle of the goal. Swansea 1-1 Tottenham.
The offside flag is raised against Emmanuel Adebayor. Indirect free kick taken by Michel Vorm.
Corner taken right-footed by Luka Modric.
Emmanuel Adebayor takes a shot. Save by Michel Vorm.
Corner taken right-footed by Stephen Dobbie, Scott Sinclair takes a shot. Luka Modric gets a block in. Joe Allen takes the inswinging corner, clearance made by Kyle Walker.
Stephen Dobbie takes a shot. Blocked by Kyle Walker.
Inswinging corner taken right-footed by Stephen Dobbie from the left by-line to the near post, clearance by Jake Livermore.
Headed effort from deep inside the penalty area by Danny Graham goes harmlessly over the crossbar.
Scott Sinclair crosses the ball.
Unfair challenge on Danny Graham by William Gallas results in a free kick. The free kick is delivered right-footed by Stephen Dobbie from left channel.
Substitution (Tottenham) makes a substitution, with Jake Livermore coming on for Scott Parker.
Substitution Jermain Defoe comes on in place of Rafael Van der Vaart.
Substitution Luke Moore leaves the field to be replaced by Danny Graham.
Luke Moore takes a shot. Brad Friedel makes a save. Inswinging corner taken left-footed by Stephen Dobbie, Effort from inside the area by Angel Rangel misses to the left of the goal.
Corner taken by Joe Allen, clearance by Younes Kaboul.
Free kick awarded for a foul by Kemy Agustien on Rafael Van der Vaart. Emmanuel Adebayor takes the free kick. Neil Taylor challenges Scott Parker unfairly and gives away a free kick. Luka Modric restarts play with the free kick.
Substitution Kemy Agustien replaces Mark Gower.
Gareth Bale produces a right-footed shot from deep inside the penalty area which goes wide of the left-hand post.
The assistant referee signals for offside against Luke Moore. Brad Friedel takes the direct free kick.
Rafael Van der Vaart takes a shot. Save made by Michel Vorm. Corner taken left-footed by Rafael Van der Vaart.
Luke Moore produces a right-footed shot from deep inside the penalty box which goes wide of the left-hand post.
Luke Moore takes a shot. William Gallas gets a block in.
Outswinging corner taken from the right by-line by Mark Gower, William Gallas makes a clearance.
Shot by Emmanuel Adebayor from deep inside the penalty area misses wide to the left of the target.
Younes Kaboul takes a shot. Michel Vorm makes a save. Corner taken left-footed by Rafael Van der Vaart, Nathan Dyer manages to make a clearance.
The second half begins.
Substitution Angel Rangel is brought on as a substitute for Ashley Richards.
45:00 +1:04 Half time
Half Time It is the end of the first-half.
Benoit Assou-Ekotto provided the assist for the goal.
43:47 Goal scored
Goal! - Rafael Van der Vaart - Swansea 0 - 1 Tottenham Rafael Van der Vaart finds the net with a goal from close in to the bottom right corner of the goal. Swansea 0-1 Tottenham.
Direct free kick taken by Garry Monk.
Booking Gareth Bale receives a yellow card for unsporting behaviour.
Effort on goal by Emmanuel Adebayor from deep inside the area goes harmlessly over the bar.
William Gallas challenges Luke Moore unfairly and gives away a free kick. Joe Allen restarts play with the free kick.
Outswinging corner taken by Rafael Van der Vaart from the left by-line, Stephen Dobbie manages to make a clearance. Effort from deep inside the area by Benoit Assou-Ekotto misses to the left of the target.
Corner taken by Mark Gower from the left by-line to the near post, Gareth Bale manages to make a clearance.
Corner taken by Rafael Van der Vaart from the left by-line, Younes Kaboul takes a shot. Save by Michel Vorm.
Raniere Sandro fouled by Stephen Dobbie, the ref awards a free kick. Free kick taken by Kyle Walker.
Scott Sinclair has an effort at goal from just outside the penalty box which goes wide of the left-hand post.
Stephen Dobbie takes a shot. William Gallas gets a block in.
Emmanuel Adebayor is caught offside. Michel Vorm restarts play with the free kick.
Emmanuel Adebayor is caught offside. Direct free kick taken by Garry Monk.
Free kick awarded for a foul by Ashley Richards on Scott Parker. Direct free kick taken by Gareth Bale.
Free kick crossed left-footed by Rafael Van der Vaart from left wing.
Booking Booking for Ashley Richards for unsporting behaviour.
Unfair challenge on Gareth Bale by Ashley Richards results in a free kick.
Free kick awarded for a foul by Benoit Assou-Ekotto on Nathan Dyer. Direct free kick taken by Ashley Richards.
Luka Modric produces a right-footed shot from just outside the box that goes wide left of the target.
Luke Moore is flagged offside by the assistant referee. Free kick taken by Brad Friedel.
Stephen Dobbie takes a shot. Save made by Brad Friedel.
Stephen Dobbie takes a shot. Kyle Walker gets a block in. Inswinging corner taken from the left by-line by Mark Gower, clearance made by Raniere Sandro. Mark Gower takes the inswinging corner, Younes Kaboul makes a clearance. Corner taken by Mark Gower from the right by-line, Scott Sinclair produces a right-footed shot from deep inside the penalty box which goes wide of the left-hand post.
Curled left-footed shot by Nathan Dyer. Save made by Brad Friedel.
Foul by Nathan Dyer on Benoit Assou-Ekotto, free kick awarded. Brad Friedel takes the free kick.
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