Watson carded a five-under 65 to start the first event of the FedEx Cup play-offs with a share of the lead, joined by fellow Americans Spencer Levin and Tony Finau, as well as Colombian Camilo Villegas.
Two-time major champion Watson could have held the outright lead if not for two late blemishes at the Plainfield Country Club in New Jersey.
Watson holed five birdies on his first nine holes after starting at the 10th and was seven under through 14.
But Watson bogeyed the sixth and ninth " his 15th and 18th holes " to settle for a five-under opening.
Spieth, playing in his first tournament as the world number one, had a tough four-over 74 to start the event.
The American looked to have settled in after also starting on the back nine, making two birdies.
But his round went wrong from then on as a double-bogey, on the par-three third, five bogeys and a birdie saw him card 40 on the front nine.
Like Watson, Levin was consistent " six birdies and a bogey making up his round " while Finau continued his decent form.
Tied for 10th at the US PGA Championship, Finau had a hat-trick of birdies (holes 10-12) and bogeys (13-15) during his round.
Villegas was at six under with two holes remaining in his first round, only to bogey the par-four eighth.
A group of six players are at four under and tied for fifth, including Danny Lee, Jason Dufner, Cameron Tringale, Russell Knox, Paul Casey and Bryce Molder.
Defending champion Hunter Mahan, who a day earlier said he was heading in the right direction, carded a 78.
Justin Rose (77) also battled, while Australian Jason Day " fresh from his win at Whistling Straits " carded a 68 despite battling a back injury.