Mount latched on to Jorginho’s angled ball, spun away from the cover and slotted into the corner in a rare moment of pure quality in Spain.
Wing-back Ben Chilwell then nipped on to a loose ball before rounding Agustin Marchesin and tapping into the empty net to put the Blues in control at the tie’s halfway point.
Pulisic broke away and blasted against the crossbar on a late Chelsea break after a smart tee-up from Giroud, but the Blues still managed to find a crucial second goal.
Jesus Corona slipped and bungled receiving a long ball, opening the door for the onrushing Chilwell.
The former Leicester left-back raced on to the ball, cut away from the covering defenders, tiptoed round Marchesin and tapped home for a fine individual effort.