The Trek-Segafredo rider clocked five minutes and 57 seconds to beat Alex Dowsett (Movistar) by two seconds and Australian Alexander Edmondson (Orica-Scott) by seven seconds.
"As soon as I saw the route with the tight bends and climb, I thought it suited the specialists, but it's also good for a complete rider like me," Felline said. "When I crossed the line, it's the first time I thought to myself at the end of a race: 'I rode that to perfection.'"
The favourites for the overall classification did not take any risks on the wet roads, with Tour de France champion Chris Froome (Sky) finishing 29 seconds off the pace and Australian Richie Porte (BMC) 33 seconds behind the winner.
“After the conditions today, I am just happy that I stayed upright," Porte said. "I felt pretty good on the bike considering I’ve had a bit of a gap between races. It was great to get the race started, and I am now looking forward to the next few road stages.”
Felline says his best win of the season "is also for Scarponi". the 2011 Giro d'Italia winner died on Saturday after a collision with a van while training near his home.
"This victory is for Michele Scarponi," Felline said. "I also want to dedicate this to another family close to me who one week before Scarponi went through the same situation. For me, the last 10 days have not been easy."
"On Sunday, a lot of people were asking me what I thought of the story of Scarponi and when I started Liege I thought maybe I could do a good result in his honour," he continued. "In the end, it was not Sunday; it was today."
Wednesday's first stage is a 173.3km mountainous ride from Aigle to Champery.