Montgomerie owned the lead by himself until suffering a bogey at the 18th hole of the Sherwood Country Club. Montgomerie and Woods both shot a 67 Friday for a 36-hole total of 9-under 133.
"I got off to a quick start and that was important," Montgomerie said. "The back nine is more tricky, but at the same time I feel the back nine you can score on as well."
Woods missed a 10-foot birdie putt at the 18th, costing him a chance for the lead.
"I played better than I did yesterday, no doubt about that," Woods said. "I putted better, but just didn't play the par-5's particularly well. I left a few shots out there, but overall, I'm very pleased with the way I hit the golf ball and especially the way I putted."