The Italian champions looked set to slip to third in the Serie A table as the game at the Stadio Friuli moved into its final quarter with the home side still a goal to the good thanks to Antonio Di Natale's 16th-minute strike.
However, recent arrival Maxi Lopez then came off the bench to equalise before then setting up Stephan El Shaarawy for the winner five minutes before the end to move Milan above Juventus into top spot.
Galliani admitted that, after a run of three games without a win in all competitions, the comeback could not have been better timed.
“Now we’re top of the table," he enthused on the club's official website. "The work done by Maxi Lopez and El Shaarawy was worth seven points because 10 minutes from the end we were third in the table.
"Now, until Wednesday, we’re on top of the league and it was important to put 6 points between us and Udinese and four points between us and [third-placed] Lazio.
"We had 14 players out today and a win in Udine was very important for the morale of the team.
"[Massimo] Ambrosini was monumental, a real captain’s performance. Maxi Lopez gave strength and presence to the attack and we’re very happy with the choice we made [in signing him]."
Galliani believes that Saturday's win at Udine could ultimately turn out to be one of the key moments in Milan's campaign.
"I think it’s a win like the win over Cagliari last year," he argued. "It’s a win that will change the fans’ mood as well as the players' and the coach’s.”
Milan now sit at the summit of Serie A on 47 points, two clear of Juventus, who have two games in hand on the Rossoneri.
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