But a foul by Jagielka on Fabregas did produce a booking – and a free-kick by Willian, which Joel Robles turned over the bar.
That prompted an Everton response, with Courtois diving to his left to save from Cleverley.
Costa, meanwhile, continued to play on the edge, once spitting on the ground close to referee Oliver, who either ignored the incident – or didn’t see it.
It was Costa, though, who almost broke the deadlock in the 58th minute.
The Spain striker moved on to a Fabregas pass, took the ball wide of Robles, but saw his shot from a tight angle travel across the face of the goal.
In a tight battle featuring strong defending, Ivanovic produced a brilliant tackle to prevent Lukaku powering clear.
But there was nothing he or Chelsea could do to prevent the Lukaku late show.