Olivier Giroud opened the scoring for the visitors before own goals from Jack Cork and Kyle Naughton and an Alexis Sanchez strike sealed the victory.
Barcelona director Pere Gratacos has insisted that Lionel Messi would not be the same player without the help of his team-mates.
The forwards put the hosts into a comfortable early lead, but Atalanta fought back strongly after the break to push Juve to the wire.
The Argentine curled a 90th minute equaliser to earn the Catalan side a point following Nicola Sanson's opener for the hosts.
The captain is now just one goal away from becoming the club's all-time top goalscorer after finding the back of the net in a comfortable win at Old Trafford.
Koke broke the deadlock before the break before a fine move was rounded off by Antoine Griezmann to put the Colchoneros in a commanding position after the first leg.
Goals from Juan Mata and Zlatan Ibrahimovic saw Jose Mourinho's men continue their unbeaten run and move level on points with fifth-place Tottenham.