Stefano Pioli has now lost three of his four league games at the helm as Cyril Thereau's first-half goal lifted the visitors up to third.
Udinese coach Andrea Stramaccioni has made a far more encouraging start to his reign and the triumph at the Stadio Olimpico came hot on the heels of Sunday's 1-0 success against Napoli.
The away side looked more threatening from the start, Luis Muriel testing goalkeeper Federico Marchetti - making his first start of the season - with an early free-kick.
Marchetti was less alert in the 22nd minute when he rushed out of goal and collided with Muriel, who picked himself up to shoot towards and empty net, only for Diego Novaretti to react and clear off the line.
Udinese deservedly took the lead after 26 minutes when Thereau fired home his first goal for the club from Silvan Widmer's excellent low cross.
Pioli introduced Filip Djordjevic at the break and he was quick to call Orestis Karnezis into action in the Udinese goal, the Greece international demonstrating a cool head and a safe pair of hands to keep hold of a powerful strike.
But, despite applying some late pressure, there was no way back for the hosts, who are now six points behind Udinese.
