Rasmus Hojlund had twice given United the lead but the Turkish team pegged them back each time before Andre Onana’s error led to Casemiro being red carded in his attempt to salvage the situation.
Mauro Icardi missed the penalty but made amends with the winner.
Questions will be asked of Onana, uncertain throughout, but much of the defence were culpable for the capitulation. Having lost to Bayern Munich in their opening Champions League game, there is much work to do to progress beyond the group stage now.
Ten Hag’s concerns are more immediate given that United have now lost six of their 10 matches this season.
Galatasaray’s first win on English soil in 11 attempts had appeared unlikely early on with Hojlund to the fore. His work set up Bruno Fernandes for a chance inside two minutes and the Dane was rewarded for his positivity with the opening goal of the game soon after.
Marcus Rashford found space out wide and his cross was met by the head of Hojlund from point-blank range. The 20-year-old striker is yet to score in the Premier League but after finding the net twice here he has three in just two Champions League appearances.
A long ball was allowed to bounce and Zaha held off the challenge of Diogo Dalot before squeezing his shot over Onana. Both defender and goalkeeper might feel they could have done more to prevent it. The result was that United lost fluency and momentum.
There were still opportunities. Mason Mount saw two chances deflected wide, one of them off his own team-mate Hannibal Mejbri. But that was nothing compared to the chance Rashford spurned early in the second half when he failed to find Bruno Fernandes.
Ten Hag appeared crestfallen on the bench, Fernandes infuriated by his team-mate’s decision to delay the centre after being put through by half-time substitute Christian Eriksen. The breakthrough then appeared to come on the hour but Hojlund was ruled offside.
There was no denying the young forward, however. With the home crowd up, Davinson Sanchez’s slip was ruthlessly punished as Hojlund ran from the halfway line, holding off his marker and then showing extraordinary composure to dink the ball into the net.
That should have broken Galatasaray but a swift counter-attack altered the mood, Amrabat and Victor Lindelof well beaten in the build-up before Kerem Akturkoglu’s crisp finish but worse was to come. A loose pass from Onana sparked United’s collapse.
Casemiro attempted to rectify the error but his rash challenge on Baris Yilmaz resulted in a penalty and a red card for the Brazilian. Icardi appeared to let United off the hook by firing wide from the spot but it was yet another defensive calamity that cost them.
Sanchez’s header forwards found Icardi free in the middle with Amrabat playing him onside from left-back and Raphael Varane nowhere to be seen. This time, Icardi finished with aplomb to spark wild scenes in the away end – and misery among United supporters.
