The 31-year-old Australian began his round at the 11th and his birdie run from the 14th gave him a nine-hole score of 7-under 28.
I played pretty nice all day, Strange said. With the weather being a bit benign, and youre getting good iron shots away and putting nicely, then theres a chance youll shoot something good.
Two of his birdies came on putts of 15 and 25 feet.
Molinari, an Italian who won the 2005 U.S. Amateur title, shot seven birdies for his 64. Jeev Milka Singh, Alvaro Velasco and Ricardo Gonzalez were tied at 65.
Because of heavy rain Wednesday, the course was shortened by 142 yards to a length of 7,210 yards.
Molinari had tendinitis last year in his left wrist but said a doctor at the AC Milan soccer club cured the problem by the unusual method of fitting a mouthguard over his lower teeth to relieve pressure on the wrist muscles.
I wasnt closing my mouth properly, Molinari said. My dad is a dentist and he didnt believe it, but it worked.
Colin Montgomerie shot a 69 with three birdies and a bogey.
He said his putting was better after discovering that he had not been looking at the hole when he putted.
When I look at the hole, it makes me follow through, he said. Ive been decelerating through the ball after being too quick on the backswing. If I look at the hole, I have to accelerate through it.