Spurs had failed to win their last five league games but got their reward for dominating the first half when Rafael van der Vaart side-footed home from 18 yards.
Gylfi Sigurdsson's looping volley beat Brad Friedel to give Swansea a second-half equaliser but Adebayor headed Spurs in front 14 minutes later before sealing the win four minutes from time with another headed goal.
Source: PA
Source: PA