The striker broke the deadlock for the visitors as early as the fifth minute when he headed home from close range after meeting a Branislav Ivanovic flick-on from a corner.
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The German side had two good chances to restore parity five minutes from half time when Kevin-Prince Boateng tested Petr Cech with a long-range effort and Neustadter came close from the resulting corner.
Torres was unlucky not to double his tally just six minutes into the second half when his close-range header came back off the crossbar.
However, the Spain international striker did complete his brace in the 68th minute. Eden Hazard started the move when he stopped a Schalke attack, went past two players and released Oscar, who then passed the ball onto Torres to slot home.
Hazard completed the scoring for Jose Mourinho's side in the 87th minute with a well-placed shot from 12 yards.