The Spanish striker – who netted 21 goals in all competitions last term – has struggled to make an impression under new manager Jose Mourinho this season.
He entered the Champions League fixture on Tuesday with just two competitive goals this season, which came against Swindon Town in the Capital One Cup and Bayern Munich in the Super Cup final.
But Torres struck twice at the Veltins Arena as Chelsea recorded a 3-0 win that saw them move top of Group E.
Torres told Uefa's official website: "I'm delighted with the win and of course my two goals.
"The three points were important after our opening defeat by Basel. We're first in the group now and still have two home games to come, so you could say we're well on track.
"The result doesn't really reflect the flow of the game. It was a lot more even than the scoreline suggests and Schalke had a lot of possession in the first half. They just failed to score. In the end I think it was our individual class that made the difference."
Torres' double will bolster his chances of a starting spot when Chelsea host Manchester City at Stamford Bridge on Sunday.