Havret, who led after every round, sank a 10-foot par putt to win the title at 14-under 278. Graeme Storm, who birdied the last, was second, and Peter Hanson (69) and David Howell (71) shared third.
Wilsons 4-under 69 meant Nick Dougherty needed to win the tournament to have a chance of making the team for the Sept. 19-21 tournament against the United States at Valhalla in Kentucky. Dougherty (70) finished seventh after bogeying three of the first six holes before recovering with six birdies.
Im very proud of myself and pleased with the weekend, especially Friday afternoon, said Wilson, who needed an eagle and two late birdies in the second round to make the halfway cut. I think at least it proved to people I can do it when I need to.
Justin Rose and Soren Hansen also made the qualifying list by staying ahead of Wilson in the top 10. The other seven automatic qualifiers were Padraig Harrington, Sergio Garcia, Lee Westwood, Henrik Stenson, Robert Karlsson, Miguel Angel Jimenez and Graeme McDowell.
Europe captain Nick Faldo selected Ian Poulter and Paul Casey as his two wild-card picks later Sunday.
Rose had struggled earlier this year, but revived his Ryder Cup campaign by finishing ninth at the PGA Championship at Oakland Hills.
I think that was the key week getting me on the team, he said. I certainly stalled in the middle of the campaign and it became hard work.
Havret said it was the first time he led a tournament after every round, but still felt nervous over the last few holes.
I felt a lot of pressure today. My drive at the last was my worst of the week, he said.
That shot finished in heavy rough and he had to play out sideways. His third shot ended in a greenside bunker, but he chipped to within 10 feet of the flag and made the putt for victory, his second in Scotland after winning the Scottish Open at Loch Lomond last year.