Rafa Benitez's side sealed their spot in Friday's Europa League semi-final draw despite losing a rollercoaster 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 hosts 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 their 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 semi-finals.
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 visitors made one change from the first leg at Stamford Bridge, 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.
But Chelsea were ahead moments later when Torres chased Frank Lampard's long ball over the hosts' defence whilst 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.
However, right on the stroke of half-time the Russian side had their best moment; 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 them plenty of belief going into the second and they made it count six minutes after the break.
Marcano towered high over Ramires and powered a header past Cech into the far post from a well-taken Rubin free kick out wide on the right.
But 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.
Rubin, though, provided an instant reply of their own. Captain Karadeniz lead by example, sneaking in behind David Luiz and heading in from close range.
The visitors then scored again 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 they had at Chelsea in the final stages but it was not enough to break the Blues' resolve, who held on to progress into Friday's semi-final draw.