Montgomerie, seeking a first victory of the season to impress Europe's Ryder Cup captain Nick Faldo enough for a wild card on Sunday, closed with a birdie before admitting to struggling on the greens as he posted a 1-over 74.
"The greens were quite soft and quite difficult," the 45-year-old chairman of the tournament said. "We've had an awful lot of rain and the greens have suffered."
The tournament is the last to count for top-10 automatic qualifying places for next month's Ryder Cup match against the U.S. at Valhalla in Louisville, Ky.
Many of the contenders for places said they were disappointed at the quality of the greens on the Centenary course, which will host the 2014 Ryder Cup.
Former European No. 1 Lee Westwood, who has already made the team for Valhalla, lambasted the greens for being bumpy and soft.
After four-putting the fifth, his 14th hole, and spoiling his score by taking 31 putts, Westwood said: "They should rip them up and re-do them, all they do is patch them up. That's my fear for the Ryder Cup here -- that they'll just go on patching them up.
"And I feel really sorry for the guys contesting Ryder Cup places. There is a lot riding on this week for them."
Havret had no qualms about his putting as he produced six birdies in his first tournament since finishing 19th in the British Open on July 20.
Last week's Dutch Open winner Darren Clarke, also seeking a Faldo wild card with a good result this week, moved within two strokes of Havret before running up bogeys on 15, 16 and 17. A closing birdie left him four behind the lead.
Of the players holding top-10 Ryder Cup positions, ninth-place Soren Hansen fared best with a 71.