The former Liverpool man tapped Cesar Azpilicueta's low cross into an empty net on nine minutes to give Jose Mourinho's men a vital away goal before the Turks rallied
After a week in which Chelsea boss Mourinho was captured on camera lamenting his striking options in what he thought was a private conversation, the visitors displayed some of their flair and vigour to score what could prove to be a priceless away goal.
They made an ideal start to their last-16 clash, silencing the vociferous home crowd by taking the lead through Torres' simple ninth-minute finish.
Making his first start since January 11, the Spaniard scored a sixth goal from his last five starts in the competition, but Chelsea failed to maintain their momentum as Gala coach Roberto Mancini altered his side's tactics and personnel.
Having dominated much of the pre-match build-up, Chelsea legend Didier Drogba was involved in Galatasaray's first threatening moment, slipping in Burak Yilmaz who failed to connect properly with his effort.
Willian then went close for Chelsea, almost taking advantage of a woeful Fernando Muslera kick to open the scoring.
However, the Gala goalkeeper managed to get his head to the shot and divert it wide in what was an unwelcome scare for the hosts.
But, in a timely reminder to Mourinho of his abilities, Torres showed his class after nine minutes by calmly stroking home from close range.
Appropriately, Mourinho had also said in midweek that "a team with 11 (Cesar) Azpilicuetas would probably win the competition", and it was the Spaniard who surged down the left wing before cutting back for Torres to finish.
In what was an open first half hour, both sides threatened in spells but it was the visitors who caused more problems on the break with the energetic trio of Willian, Eden Hazard and Andre Schurrle looking lively in particular.
The latter's cutback was put over the crossbar by Ramires after 27 minutes before Petr Cech was called on to smother Izet Hajrovic's effort soon afterwards.
As the home side enjoyed their best spell of the half, Yilmaz then had the ball in the net but saw his effort ruled out due to the presence of two balls on the pitch after a break in play.
Chelsea captain John Terry had carried the ball back onto the pitch after conceding a throw-in, and failed to get it back out of bounds before the hosts resumed play.
Terry was booked but Gala fumed that what would have been an equaliser was chalked off.
Mancini made his second change of the game at half-time, bringing Semih Kaya on in place of Hakan Balta, presumably in an attempt to limit Chelsea's fluid counter-attacks.
It appeared to work as Gala began the half brightly, although Selcuk Inan contrived to prod Wesley Sneijder's delivery against the post with the goal at his mercy before Chedjou finally did level for the Turkish side.
With neither Terry nor Cech dealing with Sneijder's corner, defender Chedjou stole in to nudge home unmarked from inside the six-yard box.
The hosts pressed for a winner in the latter stages but were unable to find a second goal - with Chelsea perhaps grateful in the end to leave the Turk Telekom Arena on level terms at the halfway point in the tie.