The points were shared at a packed Goodison Park as Everton snatched an equaliser late into injury time to lift what had been a tired contest.
Everton started strongly with Wayne Rooney using his strength well to frustrate City's defence.
And it was Rooney who played the killer ball to Steve Watson in the sixth minute which the big right back thumped his shot past an outstretched Peter Schmeichel.
But Everton could not make their superior possession pay and were caught on the back foot when City equalised in the 32nd minute.
Richard Wright fumbled an innocuous cross from Ali Benarbia which Nicolas Anelka sidefooted into an empty net.
Everton made two substitutions at half time but City came out strongest.
In the 52nd minute Benarbia jinked his way into the box, linked up well with Anelka but fired a low shot beyond the upright.
Everton were struggling to take hold of the game and Rooney showed his frustration with a vicious lunge on Marc-Vivien Foe which earned him a yellow card.
City were passing the ball well and searching for the winner.
Shaun Wright-Phillips latched onto a good throughball to send him one on one with keeper Richard Wright.
Wright smothered well but parried into the path of Foe who chipped his shot agonisingly onto the roof of the net but it was Foe who eventually broke the deadlock in the 82nd minute.
Chinese midfielder Sun Jihai curled in a perfect cross which Foe met with a clever header to flick the ball past Schmeichel.
Everton pressed for an equaliser with Schmeichel twice saving well from Steve Watson during a period of good Everton pressure.
The equaliser eventually came deep into injury time as substitute Tomasz Radzinski latched onto a Tie Li knock down to nod the ball past the stranded Schmeichel.