The former Manchester City star was superb throughout on his debut, scoring his first goal for his new club after just 23 minutes.
Udinese pulled level 10 minutes into the second half when Giampiero Pinzi's deflected effort crept in, but Milan got a chance to clinch the win from the spot in injury-time - and Balotelli stepped forward to smash the ball into the bottom left-hand corner with the last kick of the match.
The crowd, who had already been chanting Balotelli's name before the end of the first half, went wild at the winner, a strike which confirmed the star as the San Siro's new hero - and made his £19 million transfer fee seem a bargain.
The decision to award the penalty for a foul on Stephan El Shaarawy was debatable, and Udinese protested vehemently at the full-time whistle - but their voices were barely heard above the road of delight at the result.
Milan started the game with a real swagger in front of an excitable San Siro.
Balotelli was the star of the show, inspiring attack after attack as Milan pinned Udinese back in the first half. Chances came and went for El Shaarawy and M'Baye Niang before the former Manchester City striker lashed in from close range to put Milan ahead.
Balotelli's effort moments later, a stunning shot from 25 yards, was dipping into the top corner, but Padelli pulled off an equally sensational save.
Milan failed to heed the warning and Udinese levelled moments later. Catching Milan cold on the break, Luis Muriel latched onto a long ball and squared for Pinzi, whose shot deflected off Cristian Zapata and over the helpless Marco Amelia.
A series of chances were spurned by both sides, including Niang's thunderous volley that rattled the Udinese bar, before a thrilling climax.
El Shaarawy drove into the box down the left and appeared to be tackled cleanly by Thomas Heurtaux - but the referee decided to point to the spot. It was the wrong call, and Udinese's players and staff made their feelings clear before and after Balotelli sent Padelli the wrong way from the spot to cap an eventful debut for the enigmatic striker.
The result sees Milan claim their third successive win as the Rossoneri return to the top four in Serie A, while Udinese remain ninth.