Mickelson has a 54-hole total of 12-under 201. Havret, one of two co-leaders after two rounds, shot a 70. The other co-leader, Jose Manuel Lara, shot a 74 to drop five strokes off the pace.
'The difficult thing about the wind today was that it was a crosswind on a lot of holes,' Mickelson said. 'I was fortunate to get the ball in play off the tee. That was the key for me. It made for a much easier round.'
Ernie Els finished with 71 after four birdies and four bogeys to share sixth place with Lara and Mikko Ilonen.
Mickelson's round included a walk into the water at the third hole after his second shot hit the green and spun back into a pond. He wore waterproof pants to hit his submerged ball out to eight feet and holed the putt for a birdie.
Despite the wind, Mickelson managed to hit every fairway except one, the 13th.
'I should have played that more carefully for the stats because I've never hit all the fairways,' he said.
After shooting 68 in consecutive rounds, he said his confidence is increasing going into next week's British Open at Carnoustie.
'In 2004 I went in very confident in my game and finished third. But I think I need to put together one more good round here to have that same feeling,' he said.
He has a chance to win just his second event outside the United States. His only victory overseas was the Tournoi Perrier near Paris in 1993.
'I have never played as well outside the U.S. as I would like, and especially in Scotland, the home of golf,' he said. 'It would mean a lot to have a championship from here. That would really be something special.'
Havret, who led here after the third round in 2004 before dropping to 10th on the final day, had two birdies and two bogeys on the first four holes. He had all pars the rest of the way, except a birdie on the 13th.
'The past is past,' he said. 'I'm three years wiser than in 2004 but I'm playing against a better player tomorrow. I hope to play as well as I have for three days and fight as much as I can.'