Having seen Manchester United follow Arsenal and Manchester City in losing their last-16 first-leg ties 2-0, the west Londoners refused to wilt under the intense pressure brought by the raucous Turk Telecom Arena crowd.
The Blues had looked on course for victory after Torres netted in a dominant first-half display, only for Roberto Mancini's side to produce a much improved performance after the break and earn a 1-1 as poor defending allowed Aurelien Chedjou to strike home.
This was a match of many a sub-plot, varying from Chelsea favourite Didier Drogba facing his former club for the first time to former Manchester City boss Mancini coming up against Mourinho, the man who succeeded him at the Inter Milan helm.
However, the build-up focused on trouble in Istanbul as anti-government protests followed a night in which Chelsea confirmed their fans were involved in two incidents, with police warning the 1,300 travelling contingent that it was "not safe" for them to use the Metro to and from ground.
It was far from the ideal preparation - nor was the leaking of private comments from Mourinho on Samuel Eto'o and his strikers - although those that made the trip could have few complaints about the manner in which Chelsea started.
Mourinho named an attack-minded line-up and was rewarded after just nine minutes when fine play down the left ended with Fernando Torres sweeping home Cesar Azpilicueta's measured cross.
It was the first goal by an English side in Europe since December 12 and one Burak Yilmaz thought he had cancelled out as half-time approached, only for his strike from a quickly-taken throw-in to be disallowed as there were two balls on the pitch.
The other was under John Terry's arm and the Chelsea captain was booked for his part in the bizarre incident, which saw him booed off the pitch at half-time by the irate home support.
Galatasaray's fanatical support would soon be thanking Terry, though.
Minutes after Selcuk Inan hit the post, the Blues centre-back let Aurelien Chedjou out of his sights as he fired the hosts level to see the tie level when the teams resume battle in three weeks.
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.
For the first time, all that could be heard inside the stadium were Chelsea fans - but the hosts soon found their voice again.
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 a Alex Telles drive around the post before Galatasaray saw a goal disallowed in bizarre circumstances.
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 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 backpost, Chedjou lost marker Terry to volley home unmarked as the stadium erupted.
Mourinho made a quick double substitution in a bid to sure 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.