Chelsea were left to rue that miss when Heskey was on hand to direct the ball into the roof of the net after Denny Landzaat turned back David Cotterill's cross from the right.
Gallas clattered the crossbar with a powerful header in the final five minutes, the rebound falling to Vela, but the Mexican could not direct the ball goalwards, much to the frustration of his team-mates.
But Yakubu almost won the game for Everton when he fired in a speculative shot that fizzed past the post, before the Nigerian worked himself some space but was unable to produce enough power to direct the ball past Schwarzer.