Going into the game with a 1-0 aggregate lead, Chelsea blew their Czech opponents away in the first half as they went in 4-1 ahead at the break, giving them a 5-1 overall advantage.
It took just five minutes for Chelsea to double their aggregate lead as Pedro produced a sublime dinked finish after a neat one-two with striker Olivier Giroud.
And the tie was as good as over just five minutes later as the Blues doubled their lead on the night. Another smart team move set Pedro up with a simple tap-in from close range.
But the Spanish winger inexplicably fired his effort against the post, only for it to bounce up into the face of Slavia Prague defender Simon Deli and rebound into the net.
The goals just kept coming for Sarri’s rampant Chelsea, who had their third after 17 minutes with Pedro this time the provider.
He squared for Giroud to score his 10th Europa League goal of the season.
The visitors, trailing 4-0 on aggregate, pulled a goal back through captain Tomas Soucek who headed in unmarked from a corner.
But moments later Chelsea restored that advantage with their fourth goal of the night as Pedro bundled in.
Slavia Prague grabbed their second of the night shortly after half time to reduce their aggregate deficit to 5-2.
Petr Sevcik’s superb 20-yard strike was out of the reach of Chelsea goalkeeper Kepa Arrizabalaga.
And Sevcik repeated the feat from similar range in the 55th minute to give the visitors hope of an astonishing fightback.
His right-footed strike flew into the top corner as Prague made it 4-3 on the night, to cut Chelsea’s aggregate lead to 5-3.
Chelsea saw out the rest of the game though to seal their place in the last four.