Schalke were punished for slack defending as Torres opened the scoring in the fifth minute and, as the hosts pushed forward in search of an equaliser, the Spaniard netted again at the end of a second-half breakaway.
The oft-maligned forward might even have had a hat-trick, but he hit the woodwork with a header and Eden Hazard ignored the chance to pass to the Spaniard when he went through alone to seal the win late on.
Chelsea were deserving winners as they comfortably soaked up everything that Schalke threw at them in Gelsenkirchen, and the London club now find themselves level with Schalke on six points at the top of the group after Basel were held 1-1 away by Steaua Bucharest in the night's other game.
With two home matches still to come, including the return against Schalke on November 6, the 2012 European champions look well-placed to avoid a repeat of last season's group-stage exit.
"I told the players after the Basel match (which Chelsea lost 2-1) that we did garbage and we had to clean it," Mourinho told British Sky Sports television after the game.
"We did it in the best possible way with two wins away and now we are in good conditions to qualify and we can also try to finish first."
Mourinho also had praise for Torres after selecting him ahead of Samuel Eto'o, saying: "He is a hard worker. It was a surprise for me because he is not the kind of guy who hides behind the fee Chelsea paid for him. He always gives his best and he is a player I trust and respect."
Back at the ground where his Porto side beat Monaco in the 2004 Champions League final, Mourinho made a raft of changes to the team that beat Cardiff City 4-1 at the weekend.
Torres returned to the starting line-up along with German international Andre Schuerrle, while Cesar Azpilicueta was surprisingly selected as a left-back in the absence of Ashley Cole.
Schalke came into the game having lost just once in their last 10 outings - and that against Bayern Munich - but they were unconvincing in Saturday's 3-2 victory at Eintracht Braunschweig and they paid the price for a lack of concentration by falling behind with just five minutes on the clock.
With the Schalke defence sleeping, Branislav Ivanovic headed on a left-wing Frank Lampard corner and Torres popped up at the back post to convert.
Schalke enjoyed much of the possession after that but they did not really come to life until the closing minutes of the half, when Petr Cech fisted a Kevin-Prince Boateng long-ranger over the bar.
From the resulting corner, Cech produced a fine reaction save to keep out Roman Neustaedter's header, and the visitors held their lead into the interval.
It was almost 2-0 six minutes after the restart when Torres rose unmarked 14 yards out to head a Lampard free-kick off the junction of bar and post with 'keeper Timo Hildebrand rooted to the spot.
The closest Schalke came to equalising came when skipper Benedikt Hoewedes headed a good chance wide in the 65th minute, but any hopes they had of obtaining a positive result were ended three minutes later when the Premier League side doubled their lead on the break.
Hazard started the counter-attack with a pass to Oscar, and the Brazilian drove into the box and held off Japanese full-back Atsuto Uchida before squaring for Torres, who kept a cool head to round Hildebrand and score.
With the home side having lost all shape, Hazard ran through to make it 3-0 in the 87th minute, ignoring Torres to finish emphatically into the far corner and seal a fine win onChelsea's first visit to Germany since the 2012 final triumph in Munich.