The reigning champions looked set to drop below their opponents and into third place in Serie A after finding themselves a goal down to an early strike from Antonio Di Natale.
However, Maxi Lopez, a January arrival from Catania, came off the bench to equalise before then setting up Stephan El Shaarawy for the winner with just five minutes remaining.
"I’m not just content, I’m really happy because scoring for this team has always been my dream," the Argentine is quoted as saying by his club's official website.
"This win is important because it gives the team the confidence to push forward. We have to continue to find momentum and to get the three points one game at a time."
The former Barcelona man was also full of praise for the performance of El Shaarawy, who stepped up to the plate for Milan in the absence of talismanic forward Zlatan Ibrahimovic.
"El Shaarawy is young but he’s growing a lot," Maxi Lopez argued. "And this group is strong. Everyone gives their all when they get on the pitch.”
Having propelled themselves to the top of Serie A with their come-from-behind win in Udine, Milan must now turn their attention to the Champions League as they face Premier League outfit Arsenal at San Siro on Wednesday night.
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