Davide Ballardini earned his second win since replacing Luigi Del Neri as Genoa boss when Juraj Kucka nodded the hosts ahead in the first half.
Udinese had won four games from six to finally reach seventh spot last week but both Mehdi Benatia and Alexander Merkel were guilty of missing easy chances in stoppage time, allowing Catania and Roma to climb above the Friulians for the time being.
The omens were not good for Udinese when Andrea Lazzari pulled up injured within 10 minutes before being replaced by Emmanuel Badu.
The Bianconeri were quickly subdued and Genoa had a fine chance to open the scoring four minutes later, but Kucka headed a quickly-taken free-kick just wide of a post.
Genoa kept coming but Thomas Manfredini's cross from the left came up short on the run of Marco Borriello and was intercepted by Gabriele Angella.
In the 33rd minute Kucka won a corner with a ripping strike from outside the box and the Slovakian was on point to head home the resulting corner.
Udinese goalkeeper Daniele Padelli was partly to blame as he misjudged the flight of the ball and Maicosuel failed to spare his blushes by missing the target with a curling right-footed effort that dipped just over the bar.
Genoa remained the better side when play resumed after the break and Padelli was firmer in cutting out a fine left-wing cross from Juan Vargas.
The visitors nearly equalised against the run of play when Marco Rossi had to shut down a one-two between Badu and Antonio Di Natale, the latter sending his team-mate through with a cheeky backheel.
Luca Antonelli's fearsome drive shaved pain off a post and Padelli leapt onto another Borriello effort as Genoa reasserted their authority towards the final 20 minutes.
And it was nearly 2-0 but a brace for Kucka failed to materialise when Maurizio Domizzi cleared his shot off the line with Padelli at sixes and sevens.
Five minutes of stoppage time would belong to Udinese but the small travelling contingent would return north wondering how their team had not salvaged a point.
A deflected Badu effort almost evaded Sebastian Frey before Benatia defied all the odds to head wide of an open goal.
And with only Frey to beat, substitute Merkel dummied and shaped to shoot but dragged the ball beyond a post on the stroke of full-time.