The away side looked to have taken all three points following the Dutchman's opener, but the Swans eventually got what they deserved with a late equalizer courtesy of the winger
Tottenham was denied its ninth win in 11 Premier League games following a hard-fought 1-1 draw with Swansea at the Liberty Stadium on Saturday.
A forgettable first half was dominated by the home side, yet its inability to break the deadlock cost it as Rafael van der Vaart struck home from close range on the stroke of halftime.
The home side pushed for much of the second half without success, but was finally handed the break it was looking for when Brad Friedel lost the ball from a cross to allow Scott Sinclair to tap in and restore parity.
It was the home side which started the brighter of the two, with Dyer stinging the palms of Friedel early on with a well-struck 20-yard effort.
With both defenses on top in the early stages, any real threat on goal was coming via long-range efforts.
Sinclair was inches away from adding to his tally of four for the season with a beautifully curled effort. With Friedel scrambling across his line, the big American breathed a sigh of relief to see the ball clip the side netting on its way wide.
Tottenham looked to have been gifted its first real opportunity of the game when Dyer sold Michel Vorm short with a poor back pass, but the Dutch goalkeeper showed great awareness and technique to challenge Emmanuel Adebayor and deny the Togolese forward a sure goal.
Despite the lack of clear-cut chances Swansea had been the better side, and it was dealt a sucker punch on the stroke of halftime.
Following some good work on the left-hand side from Benoit Assou-Ekotto, the Cameroon international drilled a low ball into the box. The ball took a ricochet before sitting up nicely for van der Vaart, who adjusted his body to hammer home from ten yards, the ball taking a slight deflection off Williams to leave Vorm helpless.
It was Spurs who started the second half the better, Younes Kaboul with an adventurous run forward before exchanging a lovely one two with Adebayor, only to see his low effort saved by Vorm at his front post.
Tottenham had another great chance to double its lead a few minutes later. With the Swansea backline exposed, Adebayor found van der Vaart in acres of room. The Dutchman had time to take the ball in his stride and bear down on Vorm, but instead he chose to hit his shot first time, leaving the Swansea goalkeeper with a routine save.
Substitute Graham almost made an immediate impact on the game, anticipating Sinclair’s shot and trying to divert it goalwards, only to see his header flash over the crossbar with Friedel stranded.
The home side had another great chance to equalize with 10 minutes to go. Great footwork in the area from Dobbie opened up some space for the midfielder who toe poked his effort towards the back post, where Kyle Walker recovered to deny Sinclair a tap in.
From the resulting corner Sinclair saw his low effort cleared off the line by Luka Modric as the home side piled on the pressure.
With five minutes to go the home side finally got the break they deserved. Angel Rangel whipped a low ball into the box which caused havoc amongst the Tottenham defense, and after Friedel fumbled the ball, Sinclair was left with a simple tap in to send the home crowd into raptures.
The draw leaves Spurs six points behind United with a game in hand, while Swansea moves onto 20 points for the season.