The hosts left Manchester United's Old Trafford base with a stunning 3-2 win on matchday two, while Thomas Tuchel's team also came from behind to sink Copenhagen 2-1.
Match preview
Twice Rasmus Hojlund propelled Manchester United into the lead against Galatasaray, and twice the Turkish giants fought back through ex-Red Devils protege Wilfried Zaha and Kerem Akturkoglu, but victory would ostensibly be a bridge too far as Mauro Icardi fluffed his lines from the penalty spot.
However, mere moments after failing to convert from 12 yards, the Argentine attacker latched onto Davinson Sanchez's header, raced away on the counter-attack and delicately dinked the ball over Andre Onana to seal an unforgettable win over the 20-time English champions, whose cause was not aided by Casemiro's second-half sending-off.
Harnessing their comeback strengths in both of their Champions League affairs so far this season, Galatasaray also trailed 2-0 heading into the final five minutes of their matchweek one clash with Copenhagen before salvaging a point, and Okan Buruk's men sit second in the standings with their respectable four-point tally.
While Fenerbahce are sending records tumbling during their extraordinary start to the season, Galatasaray rose to the Super Lig summit and extended their winning streak to six matches in all competitions at the weekend, sinking 10-man Besiktas 2-1 as two-goal hero Icardi moved onto double figures for the domestic season.
Yet to suffer a single defeat since the new term commenced, Galatasaray have a 23-game unbeaten sequence to protect when Bayern pay a visit to their Istanbul base, and top spot in the section will be theirs if they can send Tuchel's team back to Bavaria empty-handed.
Surviving scares in both of their Champions League affairs so far, Bayern successfully fought fire with fire during their seven-goal spectacular with Manchester United, but they were staring down the barrel of defeat against an inspired Copenhagen troupe.
Following a goalless first 45 minutes, Lukas Lerager propelled the Danish Superliga holders into an unexpected lead, albeit one that lasted for all of eleven minutes as Jamal Musiala equalised before talented teenager Mathys Tel completed the Bundesliga champions' comeback.
Victory in Scandinavia marked the beginning of a perfect October for Bayern so far, as Thomas Tuchel's men boast back-to-back league wins over Freiburg and Mainz 05, scoring three goals on each occasion while only conceding to a fierce Anthony Caci drive in the latter match.
Twenty points from eight Bundesliga games represents the Bavarians' best start to a domestic season since the 2016-17 term, and a triumph on Tuesday - which would be their 20th from their last 24 Champions League away games - would set Bayern well on their way to an early knockout qualification.
In order to remain perfect in Group A, Bayern must channel the spirits of their 1972-73 European Cup crop, who drew 1-1 in their first-ever meeting with Galatasaray before progressing to the second round courtesy of a ruthless 6-0 victory in the return fixture, where the legendary Gerd Muller found the back of the net twice.
Galatasaray Champions League form:
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Galatasaray form (all competitions):
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Bayern Munich Champions League form:
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Bayern Munich form (all competitions):
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Team News
Galatasaray's success over Man United was somewhat marred by a second-half injury to Lucas Torreira, but the ex-Arsenal man has now fully recovered from that affliction and completed 85 minutes of his side's win over Besiktas before being replaced by Tanguy Ndombele.
With Torreira out of the treatment room, Galatasaray enter Tuesday's crunch clash with a clean bill of health - which has no doubt played a major part in their recent streak of success - although Sergio Oliveira will miss next month's reunion with Bayern if he is cautioned here.
However, the Portuguese lynchpin should only warm the bench this week, as Buruk keeps faith with the same starting lineup from their sensational win over Man United, all 11 of whom also featured from the off when Besiktas came to town.
In contrast, Bayern's ranks remain depleted ahead of their taxing journey to Istanbul, where none of Noussair Mazraoui (muscle), Manuel Neuer (leg), Dayot Upamecano (hamstring), Gabriel Marusic (ACL), Raphael Guerreiro (hip) or Tarek Buchmann (hamstring) should be present.
Bayern's injury crisis worsened in their recent success over Mainz, where midfielder Leon Goretzka suffered a suspected broken finger, while Serge Gnabry is closing in on a return from a fractured forearm but remains uncertain at the time of writing.
Should Goretzka not be cleared to play, Konrad Laimer - who started as a right-back against Mainz - may be shifted to a midfield role as Bouna Sarr deputises in defence, where Matthijs de Ligt was fit enough to join Kim Min-jae at the weekend following his own affliction.
Galatasaray possible starting lineup:
Muslera; Boey, Sanchez, Bardacki, Angelino; Ayhan, Torreira; Tete, Akturkoglu, Zaha; Icardi
Bayern Munich possible starting lineup:
Ulreich; Sarr, Kim, De Ligt, Davies; Kimmich, Laimer; Coman, Musiala, Sane; Kane
We say: Galatasaray 2-3 Bayern Munich
A ravaged Bayern backline should be there for the taking for an in-form Galatasaray crop, who have scored multiple goals in 11 of their last 12 fixtures and can play with the handbrake off against Tuchel's charges.