The American teed off on the 10th hole at TPC Boston in Norton, Massachusetts, bogeying the par four before producing six birdies before the turn.
Another three on his back nine saw Palmer to an eight-under-par 63 and a two-shot lead.
Keegan Bradley carded an opening-round 65, going bogey free through 18 holes - finishing with back-to-back birdies to carry momentum into Saturday.
Tied for third are Americans Webb Simpson and Chesson Hadley, alongside Australia's Jason Day, the trio on five under.
Day went bogey free, while Simpson and Hadley had six birdies and a bogey respectively.
Rounding out the top 10 are a group of five players level on four under, Americans Jordan Spieth and Bill Haas matching England's Ian Poulter, Sweden's Carl Pettersson and Russell Knox of Scotland with first-up 67s.
Defending champion Henrik Stenson shot 70, along with world number one Rory McIlroy and in-form American Rickie Fowler, while FedEx Cup leader Hunter Mahan - winner of last week's The Barclays - carded a 73.
McIlroy was looking in ominous form when he birdied three of his first four holes, but went two-over thereafter courtesy of four bogeys and two birdies.
Adam Scott, the world number two and 16th in the FedEx Cup, joined Mahan in going two-over-par to be in a tie for 65th.
Other big names to shoot over the card included Bubba Watson (72) and Phil Mickelson (74).