Andre Villas-Boas' men kept their charge for Champions League football alive as they held off a late rally from the Swans to take the points from a superb encounter
The Belgian gave the visitors an early lead before Bale added a second with a spectacular long-range goal. Michu did reduce the arrears for the Swans, but they could not find the equalizer despite dominating much of the second half.
Chico Flores returned to the Swansea defense for the first time since February, while Brad Friedel came into the side for Spurs in place of injured goalkeeper Hugo Lloris.
Tottenham made the better start to proceedings and opened the scoring inside seven minutes with an excellent goal. Bale turned in space and lofted a ball through to Vertonghen who controlled excellently before slotting past Michel Vorm with a delicate finish.
Swansea almost got on the board when Michu headed wide from a corner, but less than a minute later Andre Villas-Boas' side was two goals to the good. Vertonghen and Bale combined neatly again before the Welsh midfielder unleashed a wonderful left-footed shot with the outside of his boot which flew into the top corner.
The hosts were not deterred by their poor start however, and came agonizingly close to levelling late in the first half as Nathan Dyer crashed a header against the bar from Dwight Tiendalli's delivery.
Michael Laudrup's charges refused to halt their onslaught after the break and came close to pulling one back as Michu was denied from close range by Friedel after latching on to a quick free kick from Wayne Routledge.
Michu could not be kept down however and after a sustained period of frenetic pressure from the hosts, the Spaniard finally got his goal, heading in a Ki Sung-Yeung corner to set up a frantic finish.
That goal gave Laudrup's men the confidence to press with even more urgency but they were almost caught out on the break, Bale racing 40 yards before clipping the outside of the post with a low strike.
Spurs were clearly second best in a half dictated by the Capital One Cup winners, but they continued to create the better chances, as substitute Jermain Defoe saw a close-range effort brilliantly saved by Vorm.
There was almost late drama in added time as Bale produced an excellent tackle to deny Dyer at the death, but in truth Spurs held out with relative comfort to secure a vital victory.