With Molinari safely on the 16th green, Phil Mickelson conceded their singles match after firing his tee shot into the water, taking Europe to the magical 14.5 mark they needed to win the Cup for the fourth time in the last five.
It completed a magical year for Molinari, the British Open champion, who became the first European to win all five matches in a week — having not won any of his previous six.
Europe were effectively assured of victory when the Italian teed off as he, Henrik Stenson and Sergio Garcia were all dominant and guaranteed at least half a point — with Europe needing just one more.
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All three went on to secure wins and Swedish rookie Alex Noren completed the day's action in style when he sunk a 40-foot putt to beat Bryson Dechambeau on the last and complete a 7.5-4.5 singles victory for Europe.
It seemed a long time since the US won Friday's opening morning fourballs 3-1 but, after Europe roared back to sweep the foursomes 4-0 in the afternoon, they never looked back.
"How do you sum that up?" European captain Thomas Bjorn asked. "I just cannot describe how I feel about these 12. They have been amazing from day one and it was easy for me to guide them. It doesn't happen very often that everybody on the team scores points and so I think we got it right this week — we worked as a team."
The Europeans, playing in France for the first time, had started the day 10-6 up needing to secure four and a half of the 12 points available to win back the trophy and extend their stranglehold on home soil dating back to 1993.
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Only twice before had a team come from four down going into the singles to win — the US at Brookline in 1999 and Europe in 2012 at Medinah but another stunning comeback never really looked on the cards.
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