Luigi Del Neri's men came into the match in poor shape themselves having lost each of their last three league games, but Milan were unable to capitalise on their second-half superiority, as Udinese joined Napoli and Juventus in beating Vincenzo Montella's charges in just over a week.
Milan looked like a side eager to bounce back from those disappointing results during the early exchanges and their focused start culminated in Giacomo Bonaventura breaking the deadlock early in the first half.
The Italian was soon replaced by Serie A debutant Gerard Deulofeu due to injury and shortly after that Udinese restored parity through Cyril Thereau.
Deulofeu was one of Milan's chief threats in the second half, with his trickery and charging runs causing Udinese plenty of issues, but his final pass was often lacking.
And Udinese took full advantage of Milan's wastefulness, with De Paul's 25-yard strike finding the net and adding to the Rossoneri's woes.
Milan, who stay seventh but seven points behind third-place Napoli, showed no signs of their recent struggles early doors and were in front after eight minutes.
Suso, Milan's star man this season, was unsurprisingly crucial as he picked Bonaventura out with a pinpoint cross and the Italy international smashed home from close range.
Udinese responded well, gradually wresting control of the midfield, and they should have levelled in the 24th minute, but Davide Faraoni did not attack Jakub Jankto's cross with enough conviction at the back post and he agonisingly missed the target while colliding with the goal.
Faraoni was forced off due to that collision, while Bonaventura also had his match ended early by injury, with Deulofeu taking his place.
The changes did little to upset Udinese's rhythm, however, and they deservedly drew level just after the half-hour mark.
Emil Hallfredsson fed Thereau into the left side of the area at the end of a swift counter and the Frenchman applied an emphatic finish past Gianluigi Donnarumma.
Milan looked brighter early in the second half, coinciding with Deulofeu starting to make a nuisance of himself.
The on-loan Everton man cut in from the left and brilliantly found Suso in the far side of the area, but his eventual effort was deflected wide.
Deulofeu then picked out a clever reverse pass to Carlos Bacca after another darting run, with the Colombian's 20-yard effort fumbled by Orestis Karnezis.
Milan's inability to capitalise on their pressure ultimately contributed to their downfall.
Udinese hit Milan on the break with 17 minutes to go and De Paul beat Donnarumma from 25 yards with a low shot into the bottom left-hand corner, despite the goalkeeper getting a hand to the Argentinian's effort.
Milan almost drew level three minutes from time as substitute Gianluca Lapadula hit the post from a tight angle, but Udinese managed to see it out and hold on to the victory.