Forwards Fernando Torres and Victor Moses struck early in each half to see Chelsea through to the last four despite a valiant effort from Rubin, who scored through Ivan Marcano, Goekdeniz Karadeniz and Bebars Natcho after the break.
Chelsea, returning to the scene of their 2008 Champions League final defeat by Manchester United, took the lead after seven minutes when Torres lobbed keeper Sergei Ryzhikov from 30 metres after an exquisite through ball from Frank Lampard .
Spain striker Torres, who also netted twice in Chelsea's 3-1 victory in the first leg at Stamford Bridge, was again wearing a face mask to protect a broken nose.
The European champions were completely on top in the first half but keeper Petr Cech had to make a reflex save on the stroke of halftime to deny midfielder Natcho from eight metres.
Rubin took the game to Chelsea after the break and levelled when Marcano headed in a right-wing cross after 51 minutes.
Moses restored the London club's lead following a neat one-two on the edge of the box with Ramires before Rubin scored twice late on.
Goekdeniz Karadeniz made it 2-2 on the night with another close-range header before the Russian side converted a 75th-minute penalty through Natcho after Cesar Azpilicueta was adjudged to have pushed substitute Aleksandr Ryazantsev.
