All eyes were on the controversial striker following his £19million return to Italy and he could have netted in the opening 60 seconds on Sunday before grabbing his first Milan goal on 24 minutes.
Udinese equalised in the second half through Giampiero Pinzi and a draw looked certain until Milan were awarded a highly debatable penalty, which Balotelli coolly converted with the last kick of the match.
Balotelli had initially been named among the substitutes but started the game after Giampaolo Pazzini injured himself in the warm-up and Galliani said on Milan's official website: "He (Balotelli) is a big-time player and he started after Pazzini got injured; football is strange.
"Balotelli's two goals were a sign of fate and he could have scored after 35 seconds. I didn't see the second goal because I was in the dressing room.
"President (Silvio) Berlusconi spoke to the players and was very pleased. Our attack has a combined age of 60 and for the next 10 years I can rest easy. We have picked up 33 points in the last 15 games.
"We don't have (Lionel) Messi but we have Balotelli. This attack reminds me of Barcelona and we will see the benefit in terms of sponsors because he is only 22 and he has great potential."
Balotelli's new team-mates were also impressed. Stephan El Shaarawy, who won the controversial penalty, said: "I am pleased he scored and it is great to play alongside him. Hopefully we will do the same for the national team too."
Head coach Massimiliano Allegri also praised the "extraordinary" qualities of former Manchester City forward Balotelli.
He told the post-match press conference: "We made too many mistakes in the second half and they played well but Balotelli had a good game despite hardly knowing his team-mates.
"He has extraordinary technical and physical qualities. He can reach his full potential at Milan.
"Pazzini picked up a strain in the warm-up and seeing as Balotelli cannot play in the Champions League I decided to start him. Balotelli played the full match and has settled in immediately.
"I think there is too much pressure on him from the media and at 22 he is developing."