Rose put on a clinic with the putter and ran off four straight birdies late in his round for a 7-under 65, giving him a two-shot lead after the opening round of the Arnold Palmer Invitational.
Woods had two sloppy bogeys from greenside bunkers and didn't hit it as well as he did when he won Doral two weeks ago. But he made enough key par saves and manhandled the par 5s to scratch out a 69, a reasonable start as he tries to win Bay Hill for the eighth time and return to No. 1 in the world.
It was only the sixth time in 31 rounds at Bay Hill that Rose broke 70.
"If you had said I would shoot a 65 on the range this morning, I would have probably said, 'How many holes have I played?' And that didn't change much," Rose said. "The first five, six holes out there were a grind."
John Huh had a chance to catch him late in the afternoon, but needing a birdie on the final hole, he found a fairway bunker on No. 9 and took bogey for a 67. John Rollins and Brad Fritsch were at 68.
Rose and Woods played in the morning, the tougher side of the draw because of chilly temperatures and a strong breeze. The rough was thick without being terribly high. The hole locations were in spots Woods had not seen very often. The scores were reflective of a challenging morning until Rose and Woods began to pick up the pace on the par-5 16th.
Both made eagle from inside 15 feet — Woods hit a 9-iron for a second shot on a hole that was playing downwind — but that's where their fortunes changed. Woods came up short in a bunker, hit a poor shot and took bogey on the 17th. Rose holed a 20-foot birdie putt.
On the front nine, both made three straight birdies starting on the par-5 fourth. Rose doubled his lead over Woods on the par-3 seventh with a 12-foot birdie putt, and Woods came up short in the bunker and failed to save par.