The striker, who so often has appeared burdened by his £50million price tag, netted a scrappy opener after 16 minutes and a headed second after 70 minutes to double his tally for 2013, while Victor Moses was also on target for the Blues.
But the first leg was not altogether straightforward for last season's Champions League winners as Bebras Natcho converted a penalty after John Terry was adjudged to have blocked a shot with his arm.
Chelsea are well placed to advance to the last four in Moscow's Luzhniki Stadium - scene of their 2008 Champions League final penalty shootout defeat to Manchester United - but the away goal could yet have a crucial bearing on the outcome.
It means Chelsea's leading players must travel to Russia next week ahead of the Wembley FA Cup semi-final with Manchester City.
Chelsea interim boss Rafael Benitez will be content with the result and the performance of Torres, in particular.
Benitez was recruited, in part, to rejuvenate Torres after the pair's fruitful partnership at Liverpool and the striker has now scored 11 times since his compatriot's arrival.
Chelsea's immediate attention now turns to the quest for a Barclays Premier League top-four place and Sunday's fixture with Paolo Di Canio's Sunderland.
The Blues were hoping to replicate the performance and result of Monday's FA Cup quarter-final defeat of Manchester United, rather than last Saturday's loss at Southampton.
Captain Terry, midfielder Frank Lampard and Torres returned as three of six changes for Chelsea's third of six games in 16 days, while Yossi Benayoun made his third start of the season.
Having already eliminated Europa League holders Atletico Madrid, Rubin Kazan were seeking to add last season's European Cup winners to their list of scalps and travelled to London unbeaten away from home in the competition.
Chelsea's previous home matches in the Europa League were in the decisive second leg, but they knew they had to take the initiative ahead of next week's return.
The Blues were patient in the opening 15 minutes before the direct route paid off when David Luiz's ball from deep found Torres, who was playing in a protective face mask after suffering a broken nose against Steaua Bucharest in the previous round.
The Spaniard managed to sneak in behind Rubin captain Roman Sharonov and the pair fell tussling for the ball. Torres managed to connect while sitting on the floor to prod the ball in for his third goal in 23 games and first since the home defeat of Steaua.
The goal lifted Chelsea and the striker, who was confident enough to attempt an audacious cross soon afterwards which did not quite come off.
Natcho tested Petr Cech from 25 yards for the visitors before Chelsea doubled their advantage.
Cesar Azpilicueta crossed from the right and Moses' bouncing header was well saved, but the ball came back to the forward, who struck a swerving half-volley into the top corner.
There was a moment of concern for Chelsea when Cech caught Vladimir Dyadyun with an elbow when meeting a long ball before referee Gianluca Rocchi pointed to the penalty spot after Cristian Ansaldi's shot hit Terry on the arm.
Terry's arm appeared to be in a natural position when the ball struck it, but he was booked and Natcho sent Cech the wrong way to claim a potentially crucial away goal to the delight of a group of around 50 visiting supporters.
Ansaldi shot a yard wide from 30 yards as the visitors finished the half on the attack before bringing Jose Rondon on at half-time for Dyadyun.
Juan Mata might have restored Chelsea's two-goal lead early in the second half, but his low shot was well saved by Sergei Ryzhikov.
Rondon then shot narrowly wide as Chelsea - and the match - desperately needed a lift.
Terry attempted to provide a spark by running from deep before Eden Hazard was introduced for Moses with 25 minutes remaining.
A flick from Benayoun, who might have made way for Hazard, enabled Chelsea to surge forward as he found his former Liverpool team-mate Torres.
Torres checked, found Lampard, who in turn fed Mata, who was given time to cross.
Mata found his compatriot and Torres converted with a powerful header.
Chants for Jose Mourinho filled the cool London air, but it is Benitez's Chelsea who go to Moscow next week seeking to reach the last four.