Jose Mourinho's Chelsea took an early lead during the first leg of the last 16 tie in Istanbul through Fernando Torres.
Mourinho is a two-time winner of European football's major prize, with Porto and Inter in 2004 and 2010 respectively, and is looking to become the first manager to lift the trophy with three different clubs.
However, a shrewd tactical change by Galatasaray coach Roberto Mancini brought his side back into the contest and Aurelien Chedjou found the net from close range to earn a deserved 1-1 draw.
Mancini's successful reshuffle marked a rare moment of Champions League inspiration for the Italian, a winner of multiple domestic league titles who has failed to translate such a decorated CV into continental success.
Last May, Mancini - who led Inter to three successive Serie A crowns - was sacked by Manchester City a year to the day after delivering the club's first English title for 44 years.
A failure to progress from the group stages in two successive Champions League campaigns appeared a significant factor in City's decision, but Mancini can make a statement by guiding Galatasaray into the last eight.
Defensive midfielder Yekta Kurtulus could have a vital role to play for Galatasaray, who must stem the creative talents of the likes of Eden Hazard and Oscar to overcome an outfit that have displayed imposing form at Stamford Bridge.
In seven home European knockout matches since a 1-0 loss to Manchester United in 2011, Chelsea have recorded six wins and one draw.
Mancini appeared to overplay his hand with a four-pronged attack in the first leg, but the decision to replace Izet Hajrovic with Kurtulus enabled Galatasaray to gain a measure of control.
An engine room also likely to boast the combative qualities of Felipe Melo and Selcuk Inan could hold the key to the contest.
However, it is Galatasaray's attacking figurehead who will receive the most attention.
Didier Drogba was a talismanic presence across eight seasons with Chelsea, netting the decisive penalty as they claimed Champions League glory on his final appearance in 2012.
The veteran Ivory Coast striker is unsure of exactly how he will react to an emotional homecoming.
"I had mixed feelings," he told UEFA.com when asked about being drawn against Chelsea.
"First of all I was happy to play against my ex-club, against my friends. But at the same time it is a very special moment because I do not know what my reaction will be.
"You know that I spent eight years at Chelsea, so I really don't know. I am quite apprehensive about it."
