Mauricio Isla scored the only goal of the game on Saturday to draw Udinese level on points with Milan, who lead on goal difference after their 2-0 win at Genoa on Friday night.
Third-placed Juventus, who are a point behind, can retake the lead if they beat second-from-bottom Cesena at home on Sunday.
But while unfancied Udinese were celebrating the continuation of their stunning start to the season, giants Inter continue to struggle and remain 15th, although they could yet drop lower before the weekend is out.
The first half was a turgid affair with little in terms of goalmouth action.
Inter goalkeeper Julio Cesar saved a shot from Gabriel Torje, while Diego Milito fired off target up the other end.
The Argentine striker also sent a free-kick just over the bar while his return pass to Thiago Motta gave the Italy international a shooting chance but his precise finish was straight at goalkeeper Samir Handanovic.
Having largely played a game of containment in the first half, Udinese became especially dangerous after the restart.
The diminutive Torje won a header in the box but directed his effort straight at Cesar, while captain and emblematic striker Antonio Di Natale almost caught out Cesar with a surprise snapshot on the turn.
Mauricio Isla and Di Natale then broke clear of the Inter back line but contrived to waste the chance before the latter was wrongly ruled offside anyway.
But they found the breakthrough 17 minutes from time as Pablo Armero released Di Natale who fed substitute Antonio Floro Flores to tee up Isla to fire home.
Di Natale could have made the game safe four minutes from time after Inter captain Javier Zanetti conceded a penalty for a foul on Kwadwo Asamoah that earned him a second yellow card, but Julio Cesar saved the striker's spot-kick.
In a crazy finish, Inter were awarded a penalty a minute from time when Damiano Ferronetti was adjudged, harshly, to have brought down Milito but Giampaolo Pazzini slipped as he struck the spot-kick and sent it flying over.
Ferronetti, who was booked for the foul, then continued to protest to the referee and was shown a second yellow, meaning both teams finished with 10 men.
Napoli earned their first win in five league games to reignite their title hopes as they strolled to a 4-2 win over woeful rock-bottom Lecce.
It was just the type of game Napoli coach Walter Mazzarri, who rested several first-choice players, was looking for ahead of the southerners' trip to Villarreal in mid-week, when they may need to win to progress to the Champions League knockout rounds.
Ezequiel Lavezzi opened the scoring on 26 minutes with an individual goal, weaving infield from the left and skipping past three players before beating Lecce goalkeeper Massimiliano Benassi.
The second came just past the half-hour mark after Goran Pandev, who may have played himself into the starting line-up on Wednesday night, sent a brilliant defence-splitting pass to Edinson Cavani, who easily beat Benassi.
The third came just before the break as Lecce failed to clear their lines and Blerim Dzemaili fired home through a crowd of players from 25 yards.
Luis Muriel pulled one back for Lecce nine minutes into the second half but by then the game was already over.
Cavani put the cherry on the cake with the fourth eight minutes from time, only for Lecce's Daniele Corvia to score with his back with the last meaningful touch of the game.
Udinese keep flying as Inter woes continue
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