
Joleon Lescott headed Everton ahead.
Anthony Gardner equalized with a header of his own, but Leon Osman and Alan Stubbs with a deflected free-kick gave the visitors a two- goal lead at half-time.
A header from Dimitar Berbatov hit the bar, which turned out to be the closest Spurs came to cutting into the deficit as Everton held on to move to six points from two games, leaving Tottenham still pointless.
Not even the presence of record signing Darren Bent in the Spurs starting lineup could help the home side, and Jermain Defoe, who replaced him during the second half, went close with a shot that was well saved by Tim Howard.
The big spending of the big four - Manchester United, Chelsea, Liverpool and Arsenal - has left the rest playing catch up in recent times, but Everton manager David Moyes said he believed his side could break their stranglehold.
"We broke into it two years ago," he said. "We've been there, and I'm sure we can do it again. I've got a great deal of faith in my boys."
Tottenham manager Martin Jol was not too downbeat about the young season despite their second defeat in four days.
"We wanted to do better in the second half and not concede another goal," he said. "We did that, but we lacked a bit of creativity to break them down. It was not enough, and we have to do better, but of course there are still a lot of pages, a lot chapters to write in the story."
DPA