Genoa’s Emanuele Calaio put through his own net on 79 minutes when he made a poor connection from a free-kick by Antonio Di Natale.
Di Natale had a goal ruled out in the first half when he was adjudged to be offside.
Udinese are now unbeaten in 21 league games at home.
The defeat leaves Genoa in 14th place, with four points from five games.
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