Olesen held his nerve, however, and got up and down.
“I knew from the start it was going to be tight,” said Olesen, who entered the final round tied with Molinari one stroke behind Lee Slattery.
“I never had that final putt to win. That’s why this one feels so amazing,” Olesen added.
Molinari, the 2006 Italian Open winner, was coming off the biggest victory of his career at the BMW PGA Championship last weekend.
A bogey on the 17th — only Molinari’s second of the entire tournament — ended up being decisive.
“I don’t think I could have done more,” Molinari said. “I’m very satisfied with what I did. Complements to Olesen. He played great today and yesterday and he deserved this victory. I can’t complain. I was aggressive until the end.”
Olesen also claimed his first European Tour victory in Italy, at the 2012 Sicilian Open.
Slattery finished third, two strokes behind.