Havret had a 7-under 139 total, while Robert Rock was second after a 70. Bradley Dredge (70) and Peter Whiteford (68) shared third, two strokes behind the leader.
Montgomerie, the veteran of eight Ryder Cup teams, needs a victory or close to it to persuade European captain Nick Faldo to make him one of the two wild-card picks on Sunday. The Europeans will defend their Ryder Cup title against the Americans next month at Valhalla near Louisville, Ky.
Montgomerie was tied for 13th, five strokes off the lead.
I have to show form to have any chance, he said. If I win, I have a sporting chance but I dont necessarily have to win.
Darren Clarke, another Cup veteran seeking a wild card, struggled on the greens and shot a 73, missing three putts from within 2 feet in a round that included 34 putts.
Oliver Wilson (72) seemed to have sealed an automatic berth on the European team by just making the cut at 2 over. Wilson holds the 10th spot in the European Ryder Cup standings ' with the top 10 making the team ' and could only miss out if Ross Fisher finishes at least second or Nick Dougherty places in the top three in the tournament on Sunday.
After Fridays round, they sit in 37th and 22nd place, respectively.
I knew if I missed the cut, it was pretty much over, Wilson said. Ive given myself a chance.
Martin Kaymer, who is 11th in the cup standings, missed the cut by a stroke.
Justin Rose and Soren Hansen consolidated their eight and ninth places in the standings earlier in the day, meaning the list of 10 names who qualify automatically is all but set: Padraig Harrington, Sergio Garcia, Lee Westwood, Henrik Stenson, Robert Karlsson, Miguel Angel Jimenez, Graeme McDowell, Rose, Hansen and, probably, Wilson.
Rose shot 71 and is tied with Montgomerie. Hansen also had a 71 but hurt his wrist playing a shot out of the rough at the 12th hole. He said he did not think the injury was serious.
Wilson said he was happy after battling back from 6 over with an eagle and two birdies over the last 10 holes.
It was the biggest round of golf in my career, he said.
Montgomerie birdied four of his first 12 holes after starting on the 10th and dropped his only shot at the eighth hole, where he three-putted.
Two other contenders for wild-card selection, Paul Casey and Ian Poulter, are playing in the Deutsche Bank Championship in Boston this weekend.