Mido and Jermaine Jenas headed second-half goals to put Spurs second in the Premiership and leave Everton rooted to the foot of the table. Egyptian striker Mido glanced Jenas' cross past Nigel Martyn to break the deadlock after 58 minutes.
And Jenas headed his first goal since an £8m move from Newcastle five minutes later as Everton collapsed.
James McFadden and substitute Duncan Ferguson brought saves from Paul Robinson, but Spurs deserved the win.
It continued Tottenham's promising start to the season, but left Everton deep in crisis with only one league goal and a single win in the Premiership this season.
Spurs captain Ledley King had recovered from the dead leg sustained on England duty and was able to take his place at the heart of defence, while Young-Pyo Lee, Mido and Michael Carrick had all shaken off hamstring problems.
Everton set their stall out to frustrate Spurs and it was a ploy that worked successfully in the first 45 minutes.
Spurs' only real danger came from the height of defender Michael Dawson, who was denied by Martyn from Aaron Lennon's cross, and then saw a header blocked on the line by Nuno Valente.
Everton responded through the busy McFadden, who rounded off a fine run with a shot that was saved by Robinson.
Spurs had penalty appeals waved away when Lee went down under challenge from Matteo Ferrari as Everton defended with resilience.
But Martin Jol's side finally made the breakthrough after 58 minutes when Jenas crossed perfectly for Mido to glance a fine header beyond Martyn.
And they doubled their lead five minutes later, Jenas heading past Martyn from a pinpoint Jermain Defoe cross.
Everton, in desperation, sent on Ferguson and the giant Scot instantly brought a fine save from Robinson with a trademark header.
Tottenham coach Martin Jol: "I'm delighted. We knew this was going to be a difficult game. Everton are a very good team, despite their position in the table. "We told the players Everton would bounce back sometime, and to make sure it wasn't against us and they did that.
"At half-time we told the players to be patient because Everton are very compact. We said we had to pass the ball and do it quick, which we did.
"And I was delighted to get two headed goals from Mido and Jermaine Jenas, because we work on those things. We've had a decent start, but we have got some difficult games coming up."