Two goals in as many minutes from Steven Pienaar and Nikica Jelavic earned the Toffees a dramatic win over the North Londoners who led going into the 90th minute.
Their first real chance of the game came in the early stages of the second period, when big Belgian defender Jan Vertonghen blasted a free kick at goal and stung the palms of Tim Howard as the American goalkeeper turned the ball over the crossbar.
But the second half soon settled into a familiar tale to the opening period, with neither side creating any out-and-out chances or increasing the tempo of the game.
Everton looked short of creativity and drive after the halftime substitution of Kevin Mirallas, who appeared to suffer a relapse of the hamstring problem that has been plaguing him in recent weeks.
It took a moment of quality from Tottenham’s summer signing to break the deadlock at Goodison Park.
Dempsey received the ball just outside the Everton area and his shot at goal took a deflection off Sylvain Distin and lofted over the helpless Howard.
The goal seemed to spark the home side into life as Everton adopted a more direct approach in a bid to get back into the game.
However it was Tottenham which nearly doubled the lead when substitute Gylfi Sigurdsson saw his shot cannon off the crossbar with just five minutes left to play.
Minutes later the miss would come back to haunt Spurs as Steven Pienaar got his head on a cross from Seamus Coleman to earn an equaliser against his former club.
The comeback would be completed less than two minutes later. Nikica Jelavic pounced on a loose ball in the Tottenham area to slam home a winner for the home side.
The win moves Everton level on points with Tottenham, with the Toffees jumping to fourth in the table on goal difference.