SEVILLE, Spain, May 6, 2012 (AFP) - Overnight leader Simon Dyson of England slumped to a 76 despite opening the final round with two birdies, while Molinari had a tournament-best round of 65.
Seven birdies in the first 14 holes and then four closing pars were enough to see the 29-year-old home.
Joint-second were Dane Soren Kjeldsen and Spaniards Pablo Larrazabal and Alejandro Canizares, while Dyson fell all the way to joint-12th.
"I knew I was playing well. I just needed some putts to drop," said Molinari, who moves back into the world's top 30.
"I was also hoping the other guys would not go too far under par and everything worked out perfectly."
He is still not in a qualifying position for this year's Ryder Cup, but added: "I just have to play the same golf a few more weeks and hopefully I will be there.
"Everybody is desperate to make the team, but unfortunately for us there are only 12 spots. It's going to be hard -- there are a lot of great players in Europe at the moment."
In much easier conditions -- the first three rounds were played in wind and rain -- Dyson made quick amends for his closing double-bogey on Saturday by sinking an 18-foot putt on the first and then holing out from sand at the next.
But it all started to go wrong for the Englishman when he ran up a six at the long fifth and further bogeys came on the seventh, eighth, 13th, 15th and 17th holes.
In contrast, Molinari birdied three of the first five, then took the outright lead by two-putting the 545-yard ninth to complete an outward 32.
He picked up another shot from 10 feet at the 10th, almost holed for eagle from over 50 feet on the 13th and converted a 15-foot chance on the next hole.
"The first leaderboard I saw where I was leading was on 12, but they had a few more birdie chances than me and so I knew I needed a couple more," Molinari said.
It was comfortable in the end, though. Kjeldsen, winner of the Open de Andalucia on the course in 2009, mixed three birdies with three bogeys on the back nine, while Larrazabal and the fast-finishing Canizares were too far back.
All week the overnight leaders appeared cursed. Shaun Micheel followed his opening 67 with a 77, then Gregory Bourdy went from 66 to 80.
Leading final scores from the Spanish Open on Sunday (GBR and IRL unless stated, par 72):
280 - Francesco Molinari (ITA) 70 71 74 65
283 - Soren Kjeldsen (DEN) 71 70 71 71, Alejandro Canizares (ESP) 74 72 68 69, Pablo Larrazabal (ESP) 71 72 69 71
285 - Thorbjorn Olesen (DEN) 73 72 70 70, Jorge Campillo (ESP) 68 72 73 72
286 - Gareth Maybin 73 75 71 67, Nicolas Colsaerts (BEL) 72 72 71 71, Matteo Manassero (ITA) 70 70 76 70, Markus Brier (AUT) 74 73 72 67, Graeme Storm 70 71 74 71
287 - Marcel Siem (GER) 71 72 72 72, Richard Green (AUS) 76 72 71 68, Simon Dyson 71 69 71 76, Gregory Havret (FRA) 72 74 72 69
288 - Robert Rock 68 72 76 72, Richie Ramsay 73 71 77 67, Anders Hansen (DEN) 72 73 76 67, Jarmo Sandelin (SWE) 75 72 74 67, Peter Lawrie 71 73 71 73
289 - Carlos Del Moral (ESP) 74 73 69 73, Gregory Bourdy (FRA) 73 66 80 70, Thongchai Jaidee (THA) 73 69 74 73, Lee Slattery 74 71 74 70