First blood was drawn by experienced striker Goran Pandev, but his opener was followed by a Rodrigo De Paul penalty to see the points shared.
The Macedonian quickly opened the scoring as a powerful Kevin Strootman cross from the left came his way within point-blank range. It was one Serie A veteran to the other as Il Grifone took an eighth-minute lead.
The contest was everything but dull, and Roberto Pereyra was fouled in the six-yard box forcing Serie A debutant official Giacomo Camplone to point at the spot. De Paul converted it, high and central as the Zebrette made it 1-1 on the half-hour mark.
In hopes of completing the comeback right before half time, Fernando Llorente had a header from close range but Mattia Perin kept the scores level.
The second half saw fewer chances from both sides. In the final 20 minutes, the hosts failed to get on target while Udinese only managed one.
Man of the match Pereyra attempted a number of tireless runs and dribbles from both sides of the box, though with no fruitful end.
Two more breathtaking moments took place in the dying minutes though. Miha Zajc made an incredible solo run, getting past three players only to disappointingly hit the outside of the net in injury time
Valon Behrami also got close as Davide Ballardini’s men grew more desperate. The midfielder was sent through attempting a near-post strike only to hit the frame of the goal
The point leaves Genoa in 14th on 28 points, while Udinese sit 10th on 33.