The Italian club doubled the lead as Turkish defender Merih Demiral powered a header into the net in the 29th minute in his first Champions League goal.
Visitors Atalanta led the first half 2-0, but Manchester United turned the tables after the break.
Demiral suffered an injury and left at half time.
Man Utd forward Marcus Rashford found the bottom corner of the net to score in the 53rd minute as they narrowed the gap to one.
Then in the 81st minute, English left back Luke Shaw whipped a cross from the left to find Cristiano Ronaldo in the area. The Portuguese superstar rose and made a strong header to score the winning goal for Manchester United.
Ronaldo finished the job as Manchester United secured the narrow win.
Man Utd have six points in three matches to lead Group F.
Villarreal and Atalanta have four points each.
Young Boys are in fourth spot with three points.
Chelsea win Malmo game but lose forwards
The London team's scorers were Danish defender Andreas Christensen, Italian midfielder Jorginho and German midfielder Kai Havertz.
Jorginho successfully converted two penalties for Chelsea, and Christensen and Havertz scored one goal each for a 4-0 victory at London's Stamford Bridge stadium.
Juventus are leading Group H with nine points in three matches.
The Italian club barely beat Russia's Zenit 1-0 in Saint Petersburg as midfielder Dejan Kulusevski scored a late goal.
Second-place Chelsea have six points in the group.
Zenit have three points to come third in the standings.
Sweden's Malmo are at the bottom of Group H, losing all three of their matches so far.
Barcelona get 1-0 win at home, Pique goes down in history
Earlier Wednesday, Barcelona won against Dynamo Kyiv 1-0 at the Camp Nou stadium.
Spanish defender Gerard Pique scored the winner in the 36th minute.
Pique's volley brought three points to Barcelona and it was a historic one for him.
The 34-year-old has scored 16 Champions League goals in total, tying with Real Madrid's legendary left back Roberto Carlos in the most Champions League goals by defenders.
Pique's compatriot at Paris Saint-Germain, Sergio Ramos, who mainly plays in the center of the defense, netted 15 goals in the Champions League.
Still an active player, Ramos scored all 15 of his Champions League goals as a Real Madrid defender from 2005-2021.
Following the victory against Dynamo Kyiv, Barcelona earned their first points in Group E.
They have three points in three matches.
Group leaders Bayern Munich are in a perfect run, winning three matches to bag nine points.
Bayern Munich on Wednesday hammered Portugal's Benfica 4-0 in Lisbon as the German team's regular Leroy Sane scored twice.
Second-place Benfica have four points after the home loss.
Dynamo Kyiv racked up a point to be in last place in the group.
Barcelona - Dynamo Kyiv: 1-0
Salzburg - Wolfsburg: 3-1
Benfica - Bayern Munich: 0-4
Young Boys - Villarreal: 1-4
Manchester United - Atalanta: 3-2
Lille - Sevilla: 0-0
Chelsea - Malmo: 4-0
Zenit - Juventus: 0-1