Theo Hernandez was suspended and Tammy Abraham, Fikayo Tomori and Rafael Leão were dropped by Milan. The Rossoneri's task on Saturday became harder when midfielder Tijjani Reijnders was shown a straight red card in the 29th minute.
Fortunately for Milan, Samuel Chukwueze earned the lead in the 13th minute following yet another assist by Christian Pulisic. They held on after Udinese had two goals ruled out for offside, including one deep in stoppage time.
The Rossoneri moved level on points with third-placed Inter Milan, who play at Roma on Sunday. Juventus moved two points above them after managing to scrape a late 1-0 win over 10-man Lazio.
The radically-changed Rossoneri started brightly against Udinese and took the lead when Noah Okafor muscled his way down the left flank and rolled it across for Pulisic, who set up Chukwueze to sweep it into the far bottom corner.
Pulisic has been involved in at least one goal in seven straight league matches; producing five goals and three assists.
Milan were dominating until Reijnders was sent off for catching Sandi Lovric's heel and tripping him as the Udinese midfielder ran clear on goal.
Kingsley Ehizibue thought he headed Udinese level on the stroke of halftime but he was narrowly offside.
Pulisic came close to doubling Milan's lead in the 75th but his effort was saved by Maduka Okoye. Abraham, who had come on only three minutes earlier, injured his shoulder as he tried to bundle in the rebound and had to be taken off.
Udinese appeared to level again when Christian Kabasele headed in a rebound in the fifth minute of stoppage time. However, VAR ruled another tight offside decision in the chaotic buildup.
Lazio managed to hold out for more than an hour with 10 men before an own goal consigned them to defeat against Juventus.
Defender Alessio Romagnoli was issued a straight red card in the 24th for a tackle on Pierre Kalulu when he was clear on goal.
Despite the numerical disadvantage, Juventus didn't have a shot on target until the 81st when Lazio goalkeeper Ivan Provedel parried a curled Dusan Vlahovic effort.
The home side were gifted the winning goal four minutes later when Lazio defender Mario Gila tried to intercept a cross from Juan Cabal and succeeded only in turning it into his own net.
Vlahovic had also earlier hit the crossbar in one of Juve's few sights of goal.
A second-half double from Andrea Pinamonti saw Genoa come back from two goals down to draw with Bologna 2-2.
Bologna, who face Aston Villa in the Champions League midweek, thought they were heading for what would have been only their second win after goals from Riccardo Orsolini and Jens Odgaard.
But Pinamonti curled into the far bottom corner in the 73rd and headed in a free kick 12 minutes later.
Como drew with Parma 1-1 in a match between promoted sides.
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