Helped by a red-hot putter, Rose outshone playing partners Woods and South African Ernie Els by mixing an eagle and six birdies with a single bogey on a sunny but chilly and blustery day at "Arnie's place."
"It was a good round of golf, I kept myself out of trouble for the most part which is tough to do here at Bay Hill," Rose said. "I thought I put together a clever round of golf and capitalised with the putter today. That's as good of a putting round I've had in a long, long time."
Playing the back nine first, Rose got off to a stuttering start with a bogey at the 11th but it would be his only blemish in an otherwise sparkling round highlighted by an eagle at the par-five 16th and four straight birdies from the fourth to leave him two clear of American John Huh.
Huh spoiled an error-free round and missed a chance to join Rose atop the leaderboard when he bogeyed his final hole, the par-four ninth, after dropping six birdies for a 67.
Lurking a further stroke back on 68 are American John Rollins and Canadian Brad Fritsch.
Woods, who can reclaim the number one world ranking from Rory McIlroy with a win on Sunday, was not at his best but battled to a three-under 69 to headline a pack of 10 golfers four shots off the lead.
Woods feasted on Bay Hill's par fives, carding three birdies and an eagle on the four holes but the defending champion undid much of his good work with back-to-back bogeys at 17 and 18.
"I certainly didn't play my best, but I got around and made a few good saves out there," said Woods, who is a staggering 118-under on the Bay Hill par fives over his career. "It was so cool and the ball wasn't flying, and it presented a pretty good challenge.
"Days happen like this. It was cool this morning, and it just didn't work out but I scored well and I kept myself in the tournament."
With his confidence surging, Woods was unfazed by his uneven play, and with good reason having won seven times at Bay Hill.
"It's just one of those courses," shrugged the 14-times major winner. "I've had a few courses like that, and, fortunately, this is one of them."
FedExCup points leader Brandt Snedeker, returning to action after missing five weeks with a rib injury, showed plenty of rust as carded a four-over 76 that included a triple-bogey six at the par-three 17th.
Els, twice a winner at Bay Hill, sat out last week with a hip ailment and also struggled to a three-over 75.
But after dropping five shots on his opening five holes The Open champion recovered slightly from his horrific start by mixing three birdies with one bogey the rest of the way.