A tense first half was followed by two wonderful Rangers goals from Scott Arfield and James Tavernier before Marcao pulled one back late-on to set up a nervy finish.
From the side which defeated Motherwell in impressive fashion 5-1 on Sunday, boss Gerrard made two changes, with Ianis Hagi and Borna Barisic coming back into the side in place of Jordan Jones and Calvin Bassey.
The home side began the game well, controlling pretty much all the ball and looking to put the Turkish defence under pressure at every opportunity.
Christian Luyindama did superbly to get something on a Connor Goldson back-post header to divert it over the bar as the Gers defender rose above a cluster of bodies to get an effort on goal.
At the other end, Borna Barisic did well to nip in front of Sofiane Feghouli to see the ball behind, although the referee somehow adjudged Feghouli to have got the final touch and awarded a goal kick.
By and large, however, it was an extremely tight half, with neither side giving much away at all.
It looked like it was going to take something special to break the deadlock, and on 52 minutes, it arrived in fabulous style from Rangers.
There looked to be nothing on for James Tavernier as he surveyed the scene in front of him from just beyond halfway, but with the most outstanding ball, he picked out Ianis Hagi, who was stationed just on the edge of the ‘D’.
Running beyond him was Scott Arfield, and after bringing it under control, the Romanian found the Canadian captain who’d gone beyond the last line of red and orange shirted defenders.
Arfield’s touch too was outstanding, and he slid the ball beyond Fatih Ozturk and into the back of the net to get the all-important breakthrough.
One for Rangers was brilliant – two, and just seven minutes later – was simply outstanding from Steven Gerrard’s men. And, again, it was a goal of the very highest quality.
From one end of the field to the other they went – Allan McGregor’s short goal-kick to Goldson and then onto Tavernier to bring forward.
From the skipper, it was onto Alfredo Morelos, to Ianis Hagi and then infield to Glen Kamara. From Kamara it was wide to Ryan Kent who had Borna Barisic going beyond him.
Kamara opted to go back to Kamara though, and it was he who found Barisic to dig out a cross to James Tavernier – of course it was – to rise above Martin Linnes and nod the ball into the back of the net from close-range.
It was another move of the very highest standard of football – and highlighted the ambition and steeliness of this Rangers side to be willing to commit two full-backs so far against opposition of such note.
Morelos came close to making it three, but could find only the side netting as Kent put him in, while the Colombian had another opportunity as a Tavernier free-kick made it all the way to him, but he couldn’t convert.
Gers were showing, however, how streetwise they now are at this level, controlling the ball exceptionally well and keeping Galatasaray at arm’s length, with Allan McGregor rarely called into action.
But with three minutes to go, Galatasaray pulled a goal back – Marcao getting on the end of a header to power it across Allan McGregor and into the back of the net.
It could have been a nervy ending for Gers – but they saw it out superbly to book their place in the Group Stages.
It’s on now to the draw tomorrow which takes place at Noon.
RANGERS: McGregor; Tavernier, Goldson, Helander, Barisic; Kamara, Davis, Arfield; Hagi (Jack, 78), Kent, Morelos (Itten, 88)
SUBS: McLaughlin, Bassey, Defoe, Jones, Balogun.
GALATASARAY: Ozturk, Elabdellaoui, Antalyali, Babel (Bayram, 66), Falcao, Belhanda (Etebo, 66), Linnes, Luyindama, Marcao, Kilinc, Feghouli (Diagne, 73).
SUBS: Kocuk, Donk, Tasdemir, Sekidika.
REFEREE: Andris Treimanis