Rafa Benitez's side sealed its spot in Friday's Europa League semifinal draw despite losing a roller-coaster second leg to Kurban Berdyev's men in Moscow.
Fernando Torres' goal inside five minutes got the Blues off to the perfect start leaving the home side with a mountain to climb.
Ivan Marcano gave the Russians hope with a thumping header after the break but Victor Moses quickly put Chelsea back in the driving seat with the team's second minutes later, only for Gokdeniz Karadeniz to then level the score with another header.
Bribas Natcho gave Rubin the lead on the night from the spot but Chelsea managed to hold on thereafter to reach the semifinals.
Rafa Benitez made seven changes to the side which beat Sunderland on Sunday with Juan Mata and Eden Hazard dropping down to the bench. Nathan Ake came in to midfield to make only his second start for the Blues while Paulo Ferreira also made a rare appearance at left back.
The Russian side made one change from the first leg at Stamford Bridge as Jose Rondon replaced Vladimir Dyadyun in attack.
Rubin started the game on the front foot and came close when Roman Eremenko's shot was blocked inside the box inside the first five minutes.
Chelsea was ahead moments later when Torres chased Frank Lampard's long ball over the home side's defense while managing to lose his marker, before embarrassing Sergey Ryzhikov by cheekily lifting the ball over his head from 30 yards out.
From then on the first half was all Chelsea's. Benitez's men kept the ball for long periods and were quick to close down their opponents whenever they tried to pass through midfield.
Kurban Berdyev's men had one or two promising moments later on in the half - Alan Kasaev in particular caught the eye - but in truth the home side never looked like threatening Chelsea's lead.
Instead it was the Blues who looked more likely to add a second, something they might have managed had they been a bit more clinical in the final third.
Right on the stroke of halftime the Russian side had its best moment of the first period. Keredeniz brought down Natcho's pass inside the box but Petr Cech got down superbly to touch the Turk's prod past his far post.
That late first-half chance gave the home team plenty of belief going into the second and Rubin made it count six minutes after the break.
Marcano towered high over Ramirez and powered a header past Cech into the far post from a well-taken free kick out wide on the right.
The response from Benitez's men was emphatic as Moses, after a clever one-two with Ramires, curled a fine effort past Ryzhikov shortly after to dash any hopes the home team had of a comeback.
Rubin, though, provided an instant reply of its own. Captain Karadeniz came up big, sneaking in behind David Luiz and heading in from close range.
The Russians then pulled another back from the spot. Cesar Azpilicueta needlessly brought down Aleksandr Ryazantsev in the area allowing Natcho to dispatch his second penalty of the tie.
Rubin threw everything it had at Chelsea in the final stages but it wasn't enough to break the Blues' resolve, with the English club hanging on to move into the semifinals.