The Serie A match was a showdown between two teams coached by 2006 World Cup winners and former Milan team-mates in Gennaro Gattuso and his Zebrette counterpart Massimo Oddo.
Both men have exerted a positive impact after being appointed by their respective clubs in November, but the Rossoneri, who had Davide Calabria sent off in the 68th minute, were forced to settle for a share of spoils after the hosts battled back to earn a deserved point in front of a noisy home crowd.
Kevin Lasagna had come closest to scoring for Udinese and the striker was heavily involved when Milan's backline was finally breached, his chipped cutback hitting both Leonardo Bonucci and then goalkeeper Donnarumma before finding the back of the net.
The result saw Gattuso's eighth-placed team remain unbeaten from their last seven matches in all competitions, but stunts their progress in mounting a late charge for the Europa League qualification places, while Udinese are just two points behind them ninth spot.
Next up for Milan is a winnable fixture away to struggling SPAL, while Udinese is also on the road at Torino a day later.