Although Udinese and Napoli were tied in points after last week, Udinese managed to gain a foothold against the Partenopei.
The Bianconeri stands at third with 61 points, as fourth-place Lazio are at 59 and the recent loss to Atalanta sends Napoli to fifth with 58 points.
If Udinese manage to record a win against Catania next weekend, they will be guaranteed a spot in the group stages of the Champions League.
Relegation-threatened Genoa found themselves playing with a man down in the 29th minute, as already-booked Juraj Kucka went in on a challenge on Diego Fabbrini. Kucka was shown his second yellow, and Udinese was rewarded a free kick in dangerous territory.
Antonio Di Natale found the back of the net from a wonderfully struck free kick—his 22nd goal of the season.
Genoa ended up with nine men on the pitch after Rodrigo Palacios was sent off for insulting the referee in the 38th minute. ESPN reported that Palacios was venting his frustrations toward Emiliano Moretti, but the referee thought they were aimed at him and showed the Argentine the red card.
Udinese scored their second in the 66th minute through Antonio Floro Flores' true and powerful shot, which saw the ball in the roof of the net.
Dusan Basta looked like he was searching for Di Natale, but the cross was too pacey for the towering striker. It found the feet of Flores, who struck it for Udinese's second of the match.
Now in third, Udinese have a great chance to see themselves play in the group stages of the Champions League. There's only one game left—against 10th-place Catania, who have allowed 50 goals this season.