Joleon Lescott opened the scoring early on for the visitors, but Anthony Gardner levelled in the 26th minute.
Mikel Arteta had set up Everton's opener, and it was his cross to the back post in the 37th minute which was eventually lashed in by Osman. Stubbs extended the lead with a long-range free-kick, deflected off the foot of a defender in the wall.
It was all-out attack from the hosts in the second half, Robbie Keane testing Everton keeper Tim Howard with a drive a minute after the restart.
Dimitar Berbatov headed against the post in the next attack, after meeting Pascal Chimbonda's cross from the right. However, Everton's defence remained resolute and kept Tottenham's £40 million attack at bay for the rest of the match.