The Italian striker unwittingly turned Antonio Di Natale's 79th-minute free-kick past Genoa goalkeeper Mattia Perin.
It proved enough to hand Udinese three points on a day when they were far superior to their opponents for long periods.
Both teams went into the encounter at the Friuli stadium level on four points and looking to get their season on track.
Genoa coach Fabio Liverani made two changes to the team that held Livorno to a goalless draw at the weekend, with defender Sebastian De Maio and striker Moussa Konate starting for the first time.
Udinese coach Francesco Guidolin returned captain Di Natale to the starting line up and it paid dividends.
The hosts dominated possession and almost went in front midway through the first half.
Allan Loureiro fed Maicosuel at the edge of the area and his bullet strike went inches wide of the far post.
At the other end, Udinese goalkeeper Ivan Kelava was forced to fully stretch to clear Konate's 30-yard attempt for a corner.
On the half-hour mark, Di Natale had a goal disallowed for offside.
The home side should have gone in front before half-time but Di Natale's left-footed strike from 12 yards was kept out by Perin.
The visitors showed more determination after the restart but Udinese still had the best chances.
Shortly before the hour mark, Naldo got his head behind Di Natale's cross but his effort went off target.
Substitute Luis Muriel came closest for Udinese when his long-range attempt finished just wide of the far post.
Udinese's efforts paid off 11 minutes from time.
There was nothing Perin could do when Di Natale unleashed his free-kick and it flew off Calaio's head and crossed the goal-line.