Molinari stormed into contention with two eagles in the last seven holes to set the clubhouse target of nine under par, which Dunne was able to match with a birdie on the last.
The players returned to the 18th for sudden-death and a scrappy par was good enough to give Molinari the win after Dunne found trouble off the tee and failed to get up and down from a greenside bunker.
Woodsome Hall’s Chris Hanson repeated last year’s showing of sixth in the event and took his season’s earnings up to almost €190,000.
Last season, his first as a full member of the European Tour, hanson earned €253,254 and at this stage has left himself well placed to comfortably retain his card.
He shot rounds of 74 70 72 71 for a 287 aggregate that earned him €81,250.
Howley Hall’s Marcus Armitage’s winnings were € 5,500 after rounds of 76 70 76 79, which placed him in a tie for 66th spot.
Molinari’s previous victories both came in 2010 and the second, in the final qualifying event for the Ryder Cup, persuaded European captain Colin Montgomerie to give the former US Amateur champion a wild card for Celtic Manor.
A serious wrist injury meant Molinari played just 14 events in 2013 and, although he finished 40th on the money list the following year, he had to regain his playing rights via the qualifying school in 2015 and 2016.
“It’s fantastic,” Molinari said. “It’s been a while. I’ve been through some very hard times in the last few years and to get this I’m very very pleased. Last time I made a big putt on 17 and this time I made a big putt on 18 so it looks like I always want to keep it to the last few holes.”
After starting the day four shots off the lead, Molinari covered the front nine in level par before following a birdie on the 11th with an eagle on the par-5 12th after a brilliant approach from 250 yards.
The 36-year-old’s chance looked to have gone when he bogeyed the 16th after finding two bunkers on the tough par-4, but he birdied the 17th from close range and holed from 20ft for another eagle on the last in a superb 68.
Dunne held a two-shot lead overnight and was three clear after recovering from a bogey on the first with birdies on the second and fifth, but bogeyed the sixth and was never able to shake off the chasing pack.
The 24-year-old’s consolation was a cheque for €277,770.