The visitors took a 17th-minute lead against the run of play thanks to Leighton Baines's brilliant free-kick.
The hosts went for a winner, but were unable to break Everton down in a second half which ended in frustration.
“It was a good, hard-earned, point and I'm pleased to come here and get a draw. Before the Liverpool and Tottenham games if you would given me four points I would have taken it. I've got to give the players a huge amount of credit for their efforts."
Tottenham boss Harry Redknapp: "They are a good side, you don't ever get an easy game against Everton. But to come back from 1-0 behind shows a lot of character and they always do that, it's difficult after a tough game in midweek too."