Jim Furyk (68) and Jay Haas (66) are tied for third place at 7-under-par 135. Defending champion Davis Love III also posted a 66 to climb to minus-6. He is tied there by Chris DiMarco, who posted a 4-under 67.
European Ryder Cuppers Padraig Harrington and Miguel Angel Jimenez are one stroke further back at 5-under-par 137 after rounds of 69.
Jimenez and Love climbed to 5 under and the lead before Montgomerie teed off. The Scotsman quickly tied them atop the leaderboard as he birdied the first at Sherwood Country Club.
Montgomerie came right back with a birdie at the second to join Haas in the lead at minus-6 as Haas had birdied four of the first five holes. Monty remained hot as he drained a 5-foot birdie putt at the fourth to move to 7 under.
He continued to roll with a birdie from 12 feet out at the sixth to move two strokes clear of the field. Woods meanwhile was steady out of the gates with four straight pars.
Woods birdied the fifth and made it two straight when he birdied the sixth to get to minus-6.
Montgomerie pushed his lead over Woods to three strokes when he converted a 12-foot birdie try at the seventh to move to minus-9.
Woods started to close that gap with a 5-foot birdie on the par-3 eighth. The world No. 2 moved within one of Montgomerie with a 7-foot birdie at the ninth.
The 28-year-old Woods ripped his drive within 60 yards of the green at the 10th. He pitched to 3 feet and sank that birdie to tie Montgomerie atop the leaderboard at 9 under.
Monty, however, found a fairway bunker off the tee at the 11th. He pitched out, then hit his third to 10 feet. The 41-year-old missed that putt to fall one behind Woods.
Montgomerie nearly tied Woods for the lead with a birdie at 12, but his putt did a complete circle around the cup and spun out. The 28-time winner on the European Tour came right back to sink a 4-foot putt for birdie at the 13th and tie Woods at minus-9.
Woods dropped behind the Scotsman when he bogeyed the 14th. Woods' second shot flew the green. After taking a free drop from a storm drain, Woods flew his chip 30 feet past the cup. He two-putted for bogey to slip to 8 under.
Montgomerie hit a poor second shot to the par-5 16th. He pitched his third from the trees into the rough just short of the green. Not to worry though as he chipped in from there for birdie and a two-stroke cushion.
Woods got one back with a 9-foot birdie putt at the 17th. Montgomerie slipped back into a tie for the lead with Woods with a bogey at the last. His second shot came up short and right of the green in a hazard. He took a drop then pitched to 3 feet and sank his bogey putt to slide to 9 under.
'I got off to a quick start and that was important,' said Montgomerie. 'The back nine is more tricky, but at the same time I feel the back nine you can score on as well. The front nine people tend to be scoring better on, and I feel that there's some good holes out there on the front nine still.'
Woods had a chance to move into the lead at the last. However, he missed a 10-foot birdie putt on 18 to remain at 9 under.
'I played better than I did yesterday, no doubt about that,' said Woods, who won here in 2001. 'I putted better, but just didn't play the par-5s 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.'
Woods and Montgomerie do have their work cut out for themselves though, as no 36-hole leader has gone on to win this event.
Chad Campbell and Fred Couples share ninth place in the 16-player field at 4-under-par 138. Stewart Cink posted a 69 and is one stroke further back at minus-3.
John Daly and Todd Hamilton each shot 2-under 69 Friday to climb to even-par 142. Stephen Ames and world No. 1 Vijay Singh share 14th place at 1-over-par 143 after rounds of 69. Kenny Perry is in last place at plus-4 after his second straight 73.