Valter Birsa's 22nd-minute strike was enough to earn the Rossoneri only their third win of the season - all coming at home - and edge them closer to the top five, condemning Udinese to their fourth defeat of the campaign.
It was also a decent warm-up for Massimiliano Allegri's men ahead of Tuesday's Champions League clash with Barcelona.
In Saturday's other game, Cagliari striker Victor Ibarbo ran Catania ragged as the Sardinians marked their return to the Stadio Sant'Elia with a 2-1 win over the Sicilians.
Gonzalo Bergessio silenced the 4,000 fans permitted to see Cagliari's return home by putting the visitors ahead after just five minutes.
However, Ibarbo then took charge of the situation, scoring the equaliser before earning a penalty which resulted in a red card for Nicola Legrottaglie. The Colombian was denied from the spot by Alberto Frison, but went on to set up Mauricio Pinilla for an 84th-minute winner.