The Blues were 4-1 up after 27 minutes into the match and looked capable of scoring several more before the end.
A second-half fight back by the visitors, and two superb long-distance goals from Petr Sevcik, saw a nervy Chelsea claim a 4-3 win and a 5-3 aggregate victory.
Maurizio Sarri named a strong side at Stamford Bridge with both Eden Hazard and N’Golo Kante starting, with both rested for the first leg in Prague.
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 appeared as though it 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.
Suddenly the Blues’ cruise was under threat. And had Sevcik connected in the box when he slipped instead, their last-four place could have come under serious threat.
David Luiz got away with a cynical handball to deny Slavia a late chance, with the visitors squandering their free-kick on the edge of the Chelsea area.