Petr Sevcik scored a fine brace just after the break to make Chelsea nervous, but luckily for Maurizio Sarri, his team's stunning four-goal first-half performance ultimately gave Slavia too much to do and the Blues progressed 5-3 on aggregate.
Chelsea appeared to be in complete control of the tie by the ninth minute, as Pedro's brilliant opener was followed by Simon Deli's comical own goal, before Olivier Giroud and the Spanish forward later added further gloss to the scoreline either side of Tomas Soucek's header.
Sevcik breathed life into the tie with two long-range strikes early in the second half, but Slavia still needed another couple of goals and Chelsea did enough to see out an entertaining contest and set up a last-four meeting with Eintracht Frankfurt.
A purposeful start saw Chelsea stylishly take the lead just five minutes in, as Pedro played consecutive one-twos with Cesar Azpilicueta and Giroud before cleverly clipping over Ondrej Kolar.
It was 2-0 soon after, with fortune smiling on Chelsea. Pedro inexplicably hit the post from two yards, though it ricocheted back off Deli's face and into the net.
The excellent Giroud got in on the act with 17 minutes played, tapping in from Pedro's squared pass, only for Slavia to pull one back via a thumping Soucek header a few moments later.
Back came Chelsea, however, Pedro restoring their three-goal cushion just before the half-hour mark with a scuffed close-range finish into the bottom-right corner after Giroud's pass.
Sevcik gave Slavia a little hope six minutes after the break, with his 25-yard left-footed strike going just inside the right-hand post.
And he produced an even better effort shortly after, this time a right-footed attempt from similar distance flying into the top-left corner.
Chelsea looked to absorb pressure in the latter stages and Kepa Arrizabalaga was booked for time-wasting, a damning indictment of the drop-off in their performance, but they managed to hang on.
What does it mean? Chelsea's attitude leaves alarm bells ringing
Chelsea seemingly thought everything was all wrapped up at half-time, beginning the second period way off the pace. They never recovered the intensity showed in the first half, but fortunately for them Slavia could only get the two goals after the interval. Questions have to be asked of the hosts' mentality.
No answer to Pedro
Slavia simply could not stop Pedro. His pace and movement on the right flank made him a constant nuisance, devastating the visitors for his first and Giroud's goal. He went on to score Chelsea's fourth, and it was his effort which led to Deli's own goal. A fine outing.
Deli's difficult day
Positionally Deli was dire on several occasions, particularly in the build-up to Giroud's strike. His own goal was unfortunate, though it never would have occurred had he been tracking Pedro more competently. In all, it was a day to forget for the defender.
Key Opta facts
- Chelsea are the first English side to win 11 major European games in a single season.
- Slavia Prague are winless in their last nine European meetings with English clubs (W0 D2 L7) since winning 2-1 at home to Leeds United in March 2000 in the UEFA Cup.
- Slavia are just one of four sides to score three or more goals against Chelsea at Stamford Bridge in European competition and the first to do so in the Europa League.
- Chelsea are the second Premier League side to reach 100 goals in all competitions this season after Manchester City.
- Olivier Giroud is the first Chelsea player to score 10 goals in a single season in European football.
Chelsea return to Premier League action on Monday at home to Burnley, while Slavia travel to Zlin on Sunday hoping to retain their five-point lead at the top of their domestic table.