Dele Alli scored a pair of goals and Christian Eriksen added another as fourth-place Spurs opened up an eight-point gap over fifth-place Chelsea with the victory.
The win marked the end of an extended barren run for Tottenham, as they won at Chelsea's home ground for the first time in Premier League history.
Prior to Sunday, Tottenham had made 25 visits to Stamford Bridge without a win in the Premier League, the most that one team had played at one ground without a single victory.
That run included nine draws and 18 defeats for Spurs.
The last time Spurs won at Stamford Bridge was a 2-1 victory in February 1990 – two years before the Premier League played its first season.
Having extended their point-cushion with a historic win against the Blues, Mauricio Pochettino's side have now moved a step closer to clinching Champions League qualification.