Crowd favourite Molinari and England's Willett began the day level on 16 under par, but the Italian hit a round of 65 to edge home in a thrilling finale.
Spain's Nacho Elvira finished four shots back on 18 under par, tied for third with England's Chris Paisley.
Fellow Englishmen David Horsey, Richard Bland tied for fifth on 15 under.
Tommy Fleetwood and Scotland's Scott Jamieson were among five players tied for seventh.
Molinari, 33, hit one eagle and five birdies in Sunday's final round to become the first Italian to win his national Open twice since the event became part of the European Tour in 1972.
The victory was the Italian's fourth at a European Tour event and a first since the Reale Seguros Open de Espana in 2012.
Seven of the European Ryder Cup team, which includes Willett, were competing in Monza as they prepare to take on the United States at Hazeltine in Minnesota from 30 September to 2 October.
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Dorset County Council said the rock fall on East Beach near West Bay appears to have happened in the early hours of Friday.
It follows other landslips earlier in the year caused by winter storms.
The Jurassic Coast World Heritage team urged visitors to pay heed to warning signs and avoid "putting yourself or others at risk" by venturing close to the bottom of cliffs.
Drone pictures taken by local photographer James Loveridge show debris from the sandstone cliff spread out on the beach below.
Sam Scriven, earth science manager for the Jurassic Coast World Heritage team, said the cliffs were being monitored.
"As ever, keep your wits about you, whether you are out walking, fossil hunting, having a picnic or taking selfies.
"Always stay away from top and bottom of cliffs. Landslides and rock falls can, and do, happen anytime. Never ignore a warning sign - they are there for your safety."
Bridport Harbour also posted a warning on Facebook.
It said: "These can happen at anytime and without warning. Stay a safe distance away from the bottom of the cliffs."

The firm's progress is seen as a good indicator of global trade, as shipping carries about nine tenths of the world's trade, and Maersk Line is the world's biggest container carrier.
Maersk will probably book $3.4bn in profit for 2015, it said.
The company's shares fell 6.5% in early trading.
Shipping companies were charging about $233 to move 20-foot containers from Asia to Northern Europe, a loss-making rate according to analysis by Reuters.
Maersk blamed the drop in earnings on slender container shipping margins. It makes about half its profit from running the Maersk Line.
"Maersk Line has been hit harder than expected by low capacity utilisation due to the low volume growth in the global container transportation market," Sydbank analyst Jacob Pedersen said.
Francesco Molinari carded a six-under-par final round to beat Masters champion Danny Willett to the Italian Open title by a single shot in Monza.
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A section of cliff has collapsed onto a beach on Dorset's Jurassic Coast.
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Maersk, the Danish shipping and oil firm, said it will probably make $600m (£389m) less profit than previously thought, as global demand dropped.