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 Ottawa's 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.
Also in the group at 69 with Woods were Ryo Ishikawa of Japan, Nick Watney, Sean O'Hair and Bill Haas, who bogeyed his last two holes.
Woods played the played the par 5s in 5 under, bringing his career total at Bay Hill to 118-under par.
British Open champion Ernie Els played with Rose and Woods and disappeared quickly. The Big Easy kept pulling his tee shots and getting into trouble, dropping five shots in the opening five holes. He rallied with a 4-iron to 2 feet for birdie on the 18th, and a 9-iron to about the same tap-in range on his final hole at No. 9 to salvage a 75.
Others weren't so fortunate. U.S. Open champion Webb Simpson and two-time major champion Angel Cabrera each had 80. Masters champion Bubba Watson birdied three of his last four holes for a 74.
Brandt Snedeker, playing for the first time in five weeks because of a rib injury, took triple bogey on his 17th hole and had a 76. Snedeker's 5-iron on the 17th didn't quite clear the hazard where the sand meets the lake. Coming off his injury, he wasn't interesting in trying to gouge it out, which he probably couldn't have done, anyway. At least he had his health at the end of the round. "Encouraged," he said about his ribs.
Phil Mickelson felt terrible about his swing, and it showed. Even so, the four-time major champion made an eagle putt on the 16th to reach 1 under, only to throw those shots away with three-putt bogeys on the last two holes.
"I feel terrible walking off the course," Mickelson said, and this was right after he was randomly selected for a drug test.
For Rose, it was all about the putter — and he didn't even need any help from Steve Stricker, who gave Woods a key putting tip at Doral.
Rose began to work hard on his putting after the U.S. Open last summer, and he's had some decent rounds. At Medinah last September, he knocked in a 45-foot birdie putt on the 17th hole against Phil Mickelson, in effect the difference in Europe winning the cup.
"I dedicated myself at making a few changes and getting better at that part of the game," Rose said. "I've had some good days, no doubt. And today was probably the first real hot day I've had with the blade in a long, long time. We all know it's about consistency and that's what I'm still working towards.
"It's just fun to know that I obviously can do it, and I enjoy a lot of confidence from that."
For all his birdies, it was crucial for Rose not to drop any shots after an early bogey on the 11th, and he did that with par saves on the 14th and 15th. Just as key was the 18th, when he played short of the water for his second shot from the rough, and then made a 10-footer for par.
Putting also saved Woods.
He spent close to an hour on the range after his round to work on his driver and his irons, though he did enough right to stay in the game. It started on his opening hole when an approach from the fairway bunker went over the green and up a slight hill near the television tower. In grass still damp from the morning dew, he had to chip off the first cut of rough, down a closely mown swale to a slightly elevated green that ran away from him. The chip was so good it looked like a lag putt.
"It was one of my good ones," Woods said.
He also made good par saves around the turn that kept him at 1 under before running off three straight birdies. But it was the other bogeys that irritated him.
Woods was tied for the lead briefly after his eagle on the 16th, only to make bogey from the bunker on the 17th and another bogey on the 18th when he hit a good pitch from short of the green to 6 feet and missed the putt.
"Days happen like this," Woods said. "It was cool this morning, and it just didn't work out. But I scored well, and I kept myself in the tournament. I'm right there. Justin played a beautiful round of golf today. He had every single facet of his game working, so we had a good time out there.
"I got a lot out of this round, and I threw away a few shots as well."
David Hearn of Brantford, Ont., shot 75, while Graham DeLaet of Weyburn, Sask., and Mike Weir of Brights Grove, Ont., each shot 76.
DIVOTS: Jimmy Johnson says he will be job sharing this year as a caddie. Usually that means one player uses two caddies. In this case, it's one caddie for two players. Johnson will stay on the job for Steve Stricker, who is playing only 11 events this year, and will work for Harris English the other weeks. Johnson started with English last week at Innisbrook and is working with him again at Bay Hill. ... For the second straight week, someone made a 10. This time it was Patrick Reed, who hit two in the water on the 18th, his sixth in a back bunker and a three-putt for his 10. That was his first on tour. John Daly last week at Innisbrook made his 15th score of 10 or worse on a hole.