Chelsea, who won the first leg 1-0, doubled their aggregate lead through Pedro after only five minutes
Shortly after, Pedro somehow hit the post from close range but the ball went it on off Simon Deli to make it 2-0.
Spaniard then turned provider, putting the ball on a plate for Olivier Giroud to score a third after 17 minutes
Shortly after Tomas Soucek brought Slavia Prague back into the game on 26 minutes, Pedro netted a fourth.
He bundled ball home as Chelsea scored four in the first half of a European game for the first time since 2011.
Petr Sevcik gave Slavia hope early in the second half when he beat Kepa Arrizabalaga at his near post
Sevcik made it 4-3 on the night minutes later with a stunning second, firing beyond Kepa from outside the box.
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