Mesto strike hands Gasperini's side three points, but win is overshadowed by Toni and Palladino injuries.
Gasperini had Giandomenico Mesto to thank as the midfielder struck towards the end of the game with a superb over-head kick to ensure his side picked up the first three points of the campaign.
But, it wasn't all smiles at the Fruili as Luca Toni became the first victim to what looks like a long-term injury.
That was then compounded by Raffaele Palladino's blow. He suffered a suspected dislocated shoulder - forcing his side to play the final minutes with 10 men.
For their part, Udinese struggled from the outset and were never able to trouble the visitors.
Udinese headed into the game boosted by Antonio Di Natale's decision to remain at the club after Juventus had made an approach to sign him.
Genoa on the other hand had five new players in their starting XI with Andrea Ranocchia, Dario Dainelli, Rafinha, Miguel Veloso and Toni all featuring for the Grifoni.
It was the Friulani who started better though. Alexis Sanchez's mazy run found Giovanni Pasquale who just shaved the post with violent strike.
Eduardo made his debut in goal for Genoa and was called into action early on as he was given a speedy lesson in Calcio. Di Natale's angled blast forced the 'keeper into beating the ball to safety.
Patches of free-flowing football from the Friulani always had the opposition in difficulty. This time it was Sanchez who saw his effort saved.
Expectations are high from Veloso this term following his big money arrival for Sporting CP. He was pulling the strings for a rather pedestrian Genoa in the first half.
A quick one-two with Toni opened the door for the Portuguese midfielder to shoot, but his left foot strike from the edge of the box was ambitious and wild as it sailed over Samir Handanovic's goal.
The Grifoni should have found the breakthrough as Giuseppe Sculli popped up unmarked on the back post to head down a corner after 24 minutes, only to see Handanovic get low to palm the ball away.
And while scrappy play continued for both teams, neither were able to piece together a goal, Gasperini's doom and gloom was consigned early as he lost Toni to injury just before the end of the half. It's suspected he pulled a muscle in his left leg.
Luca whose falling: Injury blow for Toni
Gasperini wanted more, but his instructions from the bench appeared vernacular for the players as they continued to struggle in front of goal. Sculli again went close with a decent header after the restart.
Udinese responded via the odd set piece as they too found it peaky down the channels. Di Natale delivered from the corner; Domizzi's meager header too easy for Eduardo.
Again, the Portuguese international, who conceded just one goal at the World Cup, thwarted Di Natale with a fine stop as both teams pushed for a winner.
And it came 10 minutes from time as Mesto performed a spectacular over-head kick on Dainelli's knock across the box to score the first goal of the season, and with it give his side a narrow win.
Udinese travel to Inter in two weeks, Genoa host Chievo. Next week Italy are involved in the Euro 2012 qualifiers against Estonia, and then the Faroe Islands.
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