Man United failed to secure three points against Galatasary, leaving them in a thigh position in their group.
The Red Devils came into the game looking in good form after defeating Everton 3-0 at the weekend.
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However, they were only able to play a 3-3 draw, with Man United being wasteful and failing to take their chances.
Garnacho fired Man United into the lead before Fernandes scored a stunner to double their lead. Ziyech got a goal back before the end of the first half.
McTominay scored the third goal in the second half before Ziyech scored his second in the game. Man United were later shocked by Akturkoglu's equaliser to draw the game for Galatasaray.
How it happened
Galatasaray made three changes following Saturday's 4-0 win against Alanyaspor in the Turkish Super Lig.
Chelsea loanee Hakim Ziyech returned to the starting lineup with former Manchester City full-back Angelino and fellow defender Abdulkerim Bardakci also coming in.
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Ten Hag on the other hand made four changes with Rasmus Hojlund returning to Manchester United.
He replaced Anthony Martial to lead the line with Sofyan Amrabat, Aaron Wan-Bissaka and Antony also coming in.
The game started with a fast pace and Man United got the first chance of the game and took the lead.
Garnacho found space in the box and squeezed it into the roof of the net, past goalkeeper Fernando Muslera for his first Champions League goal.
A few minutes later Man United added the second when Luke Shaw played a quick ball inside to Bruno Fernandes and he carried it into the middle. He was miles out when he unleashed the strike and it sailed ferociously into the top left corner.
Galatasary got a goal back before the break when Hakim Ziyech curled the free-kick low and around the wall and the ball beat Andre Onana into the net.
The second half started and Man United restored their two-goal lead when Bruno Fernandes laid it off to Aaron Wan-Bissaka on the right and he cut it back perfectly for Scott McTominay. The Scotland international slid in and poked it past the goalkeeper at the near post.
Shortly after, Hakim Ziyech got his second goal after whipping a free-kick over the wall and Onana flapped at it, letting it go underneath his arm and over the line.
Galatasary completed the comeback when Akturkoglu took the ball in his stride in the box then absolutely fired it past Andre Onana and into the roof of the net.
The game which looked like it was there for the taken for Man United ended 3-3, leaving the Red Devils in a thigh spot.