Fernando Torres 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 vigor to score what could prove to be a priceless away goal.
The visitors made an ideal start to its 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 its momentum from the hot start, as Gala coach Roberto Mancini altered his side's tactics and personnel.
As Chelsea's threat dwindled, Aurelien Chedjou netted a second-half equalizer - with Mancini showcasing his managerial acumen against old foe Mourinho to maintain the Turks' hopes of progression.
Having dominated much of the pre-match build up, Chelsea legend Didier Drogba was involved in Galatasaray's first threat, 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.
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 its best spell of the half, Yilmaz then had the ball in the net but saw his effort ruled out because of the presence of two balls on the pitch after a break in play.
Mancini made his second change of the game at halftime, 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 John Terry nor Cech dealing with Sneijder's corner, defender Chedjou stole in to nudge home an equalizer 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.