The other three English sides in the last 16 had suffered demoralising 2-0 first-leg defeats, but it took Chelsea just nine minutes to break the deadlock in Turkey as Galatasaray's defence was pulled out of position by a swift attack and Torres tucked in a simple finish from Cesar Azpilicueta's cut-back.
However, Chelsea could not make the most of their first-half dominance and Galatasaray battled back to equalise thanks to Aurelien Chedjou in the 64th minute, setting up an intriguing return match at Stamford Bridge next month.
This was a match of many a subplot, varying from Chelsea favourite Didier Drogba facing his former club for the first time to former Manchester City boss Roberto Mancini coming up against Mourinho, the man who succeeded him at the Inter Milan helm.
But Chelsea began the match ferociously and were seemingly unmoved by intimidating surroundings.
If anything, it was the hosts looking shaken and Fernando Muslera almost handed the visitors a fourth-minute lead with a wayward clearance, only for the Galatasaray goalkeeper to react quickly to block Willian's strike.
It was a chance that highlighted the hosts' defensive vulnerability, which was exposed with just nine minutes on the clock.
Andre Schurrle slipped Azpilicueta behind former Arsenal man Emmanuel Eboue and the Spaniard pulled back for countryman Torres, who opened up his body to slot home.
Drogba, involved at both ends in the early exchanges, wasted a chance to level as a poor touch allowed Petr Cech to intercept, with Izet Hajrovic then lashing wildly over.
Most of the play, however, was at the other end, with Willian wriggling free to send a 25-yard shot at Muslera, who then saw a long-range Frank Lampard free-kick sail over his bar.
Play was halted soon after as Ramires underwent treatment, only for the patched-up midfielder to strike over soon after returning to the field.
The hosts mustered their first shot on target in the 30th minute, but Cech was more than a match for Hajrovic's low shot - the winger's last action before being replaced by Yekta Kurtulus.
It began an improved spell for the hosts, with Cech tipping an Alex Telles drive around the post before Galatasaray saw a goal disallowed in bizarre circumstances.
Burak Yilmaz thought he had struck the home side level from an acute angle, only for the goal to be chalked out as two balls were on the pitch.
Terry retreated with the ball having conceded a throw-in, only releasing it as Gala took a quick throw-in from which the Turkey international lashed home.
The Blues skipper was booked for the incident and booed off the field at half-time, with only Muslera's fine reactions denying Torres turning home after fine Eden Hazard pass six minutes after the restart.
However, Galatasaray were now on top and Gary Cahill was fortunate not to deflect a Yilmaz strike just into his own goal, before Schurrle, Ramires and Cech were all booked in quick succession.
Galatasaray were by now in the ascendancy and Selcuk Inan, another booked in that flurry of cards, hit the post from close range in the 63rd minute after Drogba nodded a header across goal.
It was a warning shot across the bows and one the Blues failed to heed.
Wesley Sneijder sent over a corner two minutes later and, with Branislav Ivanovic wrestling Drogba at the back post, Chedjou lost marker Terry to volley home unmarked as the stadium erupted.
Mourinho made a quick double substitution in a bid to shore things up, although Mancini's side were still on top and Cech did well to turn a Telles effort over the bar.
Drogba was replaced to a loud ovation by Umut Bulut as the match entered the final 10 minutes, but poor finishing ensured there would be no more goals.