The London club dominated the first half but fell behind to a superb goal from their former winger Aaron Lennon before young midfielder Dele Alli furthered his case for a place in England's midfield with a classy equaliser just before the break.
Fourth-placed Spurs had to resist intense Everton pressure at times late on as they stretched their unbeaten sequence on the road to nine league games – their best away run for 20 years.
They are six points adrift of leaders Arsenal, four off surprise package Leicester City and three behind third-placed Manchester City. They have lost only twice in the league this season, boast the best defensive record and the joint-best goal difference.
