'Today was an exciting day because I really played well,' said Woods. 'As I've been saying for a while, the things I've been working on are heading in the right direction.'
Woods' good friend Mark O'Meara posted a 66 to finish one shot back along with Jonathan Byrd and Cameron Beckman at 5 under par.
Woods has seen his lead in the world rankings shrink each week this summer, more often than not coinciding with a stellar performance by Vijay Singh. With the reigning PGA champion in the field and closer than ever to the No. 1 ranking, Woods matched his lowest opening-round score of the year to come out on top, at least for the moment.
'I like being ranked No. 1,' said Woods. 'But winning takes care of it. That's the way I tee it up each and every event is to win, period.'
Woods started on the back side at the TPC of Boston and jumped out of the gate with back-to-back birdies starting at the par-3 11th. He added a birdie at the par-4 15th and another at the par-5 18th to make the turn at minus-4.
The 28-year-old reached the green in two at the par-5 second and left himself with a long eagle try. Woods ran his putt past the hole, but converted for birdie coming back to join the leaders at 5 under. Woods found trouble at the very next hole, however, when he missed the green at the par-3 third.
Woods hit his third to 7 feet, but was unable to save par. He regained his momentum a few holes later and landed his approach inside 5 feet for a birdie at the par-4 15th.
Palmer had pulled ahead of Woods down the stretch, but the top player in the game sent his second shot to the back of the green at the par-5 seventh and two-putted for birdie to regain a share of the lead. Woods then parred his way in to hold a piece of the 18-hole lead for the first time this season.
'It's certainly nice to have that opportunity where I don't have to go out there and shoot a round like this just to try and make the cut,' said Woods. 'It's been nice to go out there and just hit a bunch of good golf shots.'
Palmer, a rookie on the PGA Tour, took advantage of the par-5s on the front nine, starting at the second when his 6-iron approach stopped within 15 feet of the hole. Palmer drained the eagle putt, but stumbled to a bogey at the sixth.
'I've just been struggling putting and just tried to come here this week and have a good time and have fun today,' said Palmer.
At the par-5 seventh, Palmer hit his second shot in a greenside bunker but walked away with eagle after his shot from the sand found the bottom of the cup. He then birdied two in a row from the eighth to go out in 31.
Palmer ran off a string of pars on the back side until his second shot to the par-5 18th bounced off the back edge of the green. The 27-year-old chipped to 5 feet and rolled in the birdie putt for his share of the lead.
'It's been fun this year,' said Palmer. 'It's been a struggle at times, but then again, I've had a lot of good things coming out of this year. It's getting better and I'm looking forward to that one good week.'
Charles Howell III carded a 4-under 67 to join John Rollins, Craig Perks, Deane Pappas and Billy Mayfair in a tie for sixth. Singh was one shot further back in a group at 3-under-par 68 that includes Zach Johnson, Aaron Baddeley and Shigeki Maruyama.
Defending champion Adam Scott, who earned his first career victory on the PGA Tour at this event last year, posted a 2-under 69 to finish four shots off the pace.