Chelsea saw six shots and one header sail wide in the first half, and it took a top-level save from Jose Sa to thwart Pulisic's long-range strike towards the top corner.
In first-half injury time, though, Havertz popped up at the far post to head home Mount's lofted cross.
Chelsea wasted little time to double that lead after the restart. Pulisic traded passes with Mount to skip into the box on the inside left, then deliver a deft finish to beat the advancing Sa.
Former Chelsea striker Diego Costa made his debut for Wolves and claimed the biggest reception of the day when he was substituted, taking a lap of honor as he slowly walked along the touchline toward the Wolves dugout.
Brojca's goal came when fellow substitute Mateo Kovacic threaded through to the forward, who cut back from the defensive cover before drilling into the net.