Chelsea, who are in Europe's second-tier competition after failing to clear the group stage of the Champions League they won last year, were playing their third game in six days and fielded several players normally left on the bench.
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Torres, who has struggled to keep his place in the starting 11, opened the scoring in the 16th minute when he ran on to a long pass lofted over the defence by David Luiz and poked the ball home after tangling with a defender.
Victor Moses doubled Chelsea's lead in the 32nd minute, controlling a poor clearance with his chest before drilling a shot into the top corner.
At that point Chelsea seemed in control of the tie.
However, Rubin grabbed an away goal in the 41st minute when Israeli midfielder Bebras Natcho scored from the penalty spot after John Terry had blocked a shot by Cristian Ansaldi with his arm.
Chelsea almost restored their two-goal lead shortly after half-time when Rubin goalkeeper Sergey Ryzhikov dived to save a low, curving shot by Juan Mata.
Torres gave Chelsea breathing space when he met a cross from fellow Spaniard Mata with an emphatic header in the 70th minute.
Rubin eliminated holders Atletico Madrid in an earlier round and beat Inter Milan in the group stage of the competition.
The second leg will be played on April 11.
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