Maurizio Sarri's men appeared out of sight within 20 minutes. Pedro's stylish lob over goalkeeper Ondrej Kolar opened the scoring after six minutes at Stamford Bridge and Simon Deli put through his own net to double the hosts' advantage.
Olivier Giroud added the third in the 17th minute for a 4-0 aggregate lead.
Any thoughts of a stroll were soon abated though. Tomas Soucek pulled one back for the visitors. But within seconds Pedro made the Czechs pay for their impertinence with his second of the game.
But a 5-1 aggregate lead was shaved within three second half mintues when Petr Sevcik bagged a brace.
From then on, the home faithful were decidedly nervy but Prague failed to add to their tally and exited the competition.
Valencia were, in comparison to Chelsea, ruthlessly efficient. Leading 3-1 from the first leg in Villareal, Toni Lato scored for Valencia to give them control over their fellow Spaniards.
Daniel Parejo added Valencia's second nine minutes after the restart. There was no kickback from Villareal.
And there was little response too from Napoli. Carlo Ancelotti's side trailed 0-2 from the first leg against Arsenal at the Emirates on 11 April.
The expected onslaught at the Stadio San Paolo failed to materialise.
Alexander Lacazette punished Napoli's lack of ambition. He scored the only goal of the game direct from a free-kick just before half-time to give the north Londoners a 3-0 aggregate victory and a semi-final showdown against Valencia.
Chelsea will face Eintracht Frankfurt after they staged a thrilling comeback against Benfica.
The Germans went into the second leg after a 4-2 mauling in Portugal.
But a strike in each half from Filip Kostic and Sebastian Rode gave them the two goals that took them into the last four on the away goals rule.