Sublime goals from Jan Vertonghen and Gareth Bale put Spurs in pole position to get back to winning ways after back-to-back league defeats.
However, the home side rallied in the second half and got themselves back in it thanks to Michu, who headed his 11th home league goal of the season to ensure a nervy end to the game for the travelling Spurs faithful.
The visitors managed to hang on though and moved up to third thanks to results elsewhere, whilst the Swans remain comfortable in ninth.
It did not take long for Spurs get into their stride, and the in-form Bale turned provider for a change, lofting a sublime pass on the turn into the path of the onrushing Vertonghen, who plucked the ball out of the air and prodded a shot past Michel Vorm.
With only one clean sheet in the last nine Premier League games, Spurs boss Andre Villas-Boas will not have been sitting comfortably, but just 15 minutes later the same two players combined to devastating effect to double the visitors' lead.
Vorm's poor clearance found its way to Vertonghen, who carried the ball forward, drilled a pass into the feet of Bale and he took one touch before lashing an unstoppable shot past the helpless Swansea keeper.
Michael Laudrup needed a response from Swansea, and the shell-shocked home side upped their game and started to create more opportunities, the best of which was wasted by Nathan Dyer, who could only head Dwight Tiendalli's pinpoint centre onto the underside of the bar from close range.
The home side continued to increase their intensity in the second period, and looked much more of a threat going forward.
A quickly taken free-kick caught Spurs sleeping, but Brad Friedel reacted well to smother Michu's prod towards goal.
The Swans' pressure did eventually tell on 71 minutes as Michu outjumped a flat-footed Michael Dawson to head a right-wing corner into the bottom corner.
Bale did almost make it three, clipping the bottom of the post after a mazy run, but arguably his most important contribution was a last-ditch block in injury-time to thwart Dyer when he looked odds-on to net a dramatic equaliser.