After Galatasaray star Muhammed Kerem Akturkoglu cancelled out Rasmus Hojlund's second goal of the night in the second-half, Onana made an awful mistake.
After trying to play out from the back, the ex-Inter Milan star's pass was easily cut out by Dries Mertens, who raced into the United box.
Casemiro came sliding in from behind and was sent off as a result, giving away a penalty, but Mauro Icardi dragged his effort wide.
But if the Argentine gave United a lifeline, Onana threw it away just moments later.
When a cleared header from Davinson Sanchez inexplicably found its way to Icardi, the former Paris Saint-Germain star found himself one-on-one with the United No. 1.
READ MORE ON MAN UNITED
Zaha cups his ears to Old Trafford as ex-Man United man takes advantage of poor defending
Valencia issue hands off warning to Man United and Newcastle for wonderkid
The striker attempted a chip but it barely lifted off the ground, though it was still enough to beat Onana, who was already nearly seated as the Turkish side claimed an unlikely 3-2 win.
Sofyan Amrabat was the guilty party for playing Icardi onside, standing about 10 yards behind the rest of his defenders.
It gave Gala the chance of a lifetime, something Icardi did not mess up, having already smashed his earlier penalty from minutes before wide.
While United huffed and puffed, they could not get back in the game and they suffered yet another defeat in the Champions League.
Most read in Champions League
Lens 2-1 Arsenal LIVE: Wahi gives hosts lead as Gunners shocked after Saka injured
Man United 2-2 Galatasaray LIVE: Hojlund brace cancelled out by defensive horror show
Fans marvel at Bellingham's solo goal and Vinicius Jr loved it so much he took 'picture'
Saka goes off injured as Arsenal boss Arteta's Champions League gamble backfires
It has left them with no points after two matches, having lost to Bayern Munich in their opener, where Onana was also at fault for another clanger.
And it started so brightly for the Red Devils, who saw Marcus Rashford and Hojlund combine beautifully for the opener.
However, Wilfried Zaha returned to haunt his old side when his deflected effort left Onana grasping desperately at the air.
Hojlund returned in the second-half to net another, latching onto a mistake from Sanchez, who had slipped to allow the Dane to race on goal.
That was moments before United pressed the self-destruct button, leaving Erik ten Hag looking furious in the rain.
There were boos from the home fans at full-time but they were drowned out by the vociferous support of Turkish fans in the away end.
But with two wins in seven matches, the pressure will continue to ramp up on Ten Hag.