Eric Bailly brilliantly denied Atalanta a goal with a brave diving challenge with the score at 1-0 before Cristiano Ronaldo equalised in first-half stoppage time.
Paul Pogba carelessly gave away possession in a dangerous position in the defending final third, after being dispossessed the ball bounced for Duvan Zapata and with the goal at his mercy he saw his effort blocked by the shoulder of the Ivorian.
The hosts found an early breakthrough when Josip Ilicic's strike squeezed through Luke Shaw's legs before squirming beneath David de Gea.
Ole Gunnar Solskjaer maintained the 3-4-2-1 formation that comfortably beat Spurs 3-0.
For Bailly, it was a first Champions League start in two years as he deputised for the injured Victor Lindelof, who received a knock in the build-up for the trip to Bergamo.
United fans as a result were singing the defender's praises for the brave piece of evasive action.
Despite being a goal down, United had their chances with Scott McTominay hitting the post as well as Cristiano Ronaldo and Marcus Rashford having efforts.
But they were dealt another defensive blow on the stroke of half-time after Raphael Varane limped off but it didn't stop United finding an equaliser as the 36-year-old continued his rich vein of form in front of goal in the Champions League.
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