Villa performed well in the first half but several excellent saves from Edouard Mendy meant they failed to register any goals.
Lukaku opened the scoring for Chelsea after 15 minutes after dancing around Axel Tuanzebe
Villa started the second half strongly with Mendy forced into another good save from Tuanzebe.
They were left to rue their missed chances when Kovacic doubled Chelsea’s lead on 49 minutes.
Tyrone Mings attempted to pass the ball back to Steer but hit it short. Kovacic stole it and hit a shot into the bottom left corner.
Lukaku sealed the win on 93 minutes after Cesar Azpilicueta went on a run down the right. He found Lukaku who struck a left-footed shot from outside the box into the net.