United boss Ole Gunnar Solskjaer fielded a youthful XI, given the Red Devils had already sealed their progress to the knockout phase in Group L.
Despite that Jesse Lingard put United ahead early with a 10th minute strike.
United youngster Tahith Chong missed from point blank range before the hosts hit back in the second half.
Dimitri Shomko levelled in the 55th minute, before an own goal from Dishon Bernard seven minutes later.
United remain top of Group L with 10 points from five matches, while Astana claimed their first points of the campaign.
AZ Alkmaar drew 2-2 at home with Partizan Belgrade in the other group game.
Andre Horta had put the hosts ahead early, before Raul Jimenez headed the equaliser on 13 minutes.
The Gunners had led after Pierre-Emerick Aubameyang’s first-half goal but Daichi Kamada netted a second-half double to seal the win in front of a disgruntled Emirates crowd, with plenty of empty seats.