Olesen carded a flawless closing 64 at Gardagolf to finish 22 under par, a shot ahead of home favourite Molinari, who had won the BMW PGA Championship at Wentworth last week.
The two players had been tied for the lead with two holes remaining, but Molinari followed four straight birdies by dropping only his second shot of the week on the 17th and Olesen birdied the same hole in the group behind to take a two-shot lead.
The Italian refused to throw in the towel and holed a curling birdie putt on the last from 40 feet to complete a 65 and pile on the pressure, but Olesen got up and down from a greenside bunker for par to secure the first prize of £874,000 in the second Rolex Series event of 2018.
“This is my first time coming from behind to win so that’s very special to me,” Olesen said after a victory which takes him just outside the automatic qualifying places for September’s Ryder Cup, when fellow Dane Thomas Bjorn will captain the European side. “I always wanted to come up the leaderboard and take the trophy. I’ve never had that putt on the last to win a tournament so that’s why this one feels so amazing. I was standing on the 18th tee and heard I was two in the lead, that’s why I picked the 5-wood from the tee. I thought that would give me a good chance to make four and worst case I would make five, but I was standing there and saw that great putt he [Molinari] holed and that put some pressure on me.”
Molinari said: “I’m super happy to be honest. It’s been an amazing week. I think I’ll never forget the run of birdies today on the back nine. Obviously a shame about 17, but I can’t complain. The putt on 18 was just unbelievable. It’s not really a putt that you think about making, but in those circumstances you want to give it a chance. Sometimes there’s just something in the air that makes special things happen.”
England’s Lee Slattery finished alone in third after a closing 67, despite having to get a replacement caddie after 13 holes after Max Cunningham was unable to continue.
“I hope he’s all right,” Slattery said. “He had a really bad back. Going up one of the hills he was struggling to breathe a little bit and we switched caddies, which affected me a little bit. I hit a poor drive off the next and I didn’t hit many poor drives today. Just cost me a couple of shots and they were crucial at the end. But I’m delighted to finish 20 under par and third in a Rolex Series Event, that’s a big stepping stone for me. To come here and play like I did and secure my rights for next year, there’s so many things I’ve done this week in just one week.”