Mickelson, playing in Scotland ahead of this week's British Open, lost in a playoff to Havret at Loch Lomond after making bogey at the 72nd hole to fall back into a tie with the Frenchman.
He climbed one spot to No. 2 in the rankings, bumping Jim Furyk to third.
Tiger Woods, of course, remained the top-ranked golfer in the world heading into his title defense at the British Open.
Ernie Els received a bump based on his performance in Scotland, where he finished a shot back of Mickelson and Havret. He moved up a spot to No. 4, dropping Adam Scott to fifth.
Vijay Singh, Henrik Stenson, Geoff Ogilvy, Luke Donald and Padraig Harrington rounded out the top 10 in the same positions they held last week.
Retief Goosen, K.J. Choi, Sergio Garcia, Rory Sabbatini, Master champion Zach Johnson, Steve Stricker, U.S. Open winner Angel Cabrera, Paul Casey, Trevor Immelman and Niclas Fasth filled out the rest of the top 20.
Havret moved up 205 places to No. 115 following his win, while Jonathan Byrd parlayed a victory at the PGA TOUR's John Deere Classic into a 41-spot bump to No. 68 this week.