After a bogey at the 15th, the British Open champion made amends by sinking a 40-footer for birdie at the 16th and finished the day at six-under 134.
Fellow Americans Dustin Johnson (69) and Rickie Fowler (66), and Venezuelan Jhonattan Vegas (65) are also six-under in the first of the PGA Tour's four FedExCup playoff events.
Spieth said he had decided during his pre-round routine to ignore any technical putting thoughts.
"I was messing around a little with alignment and ball position," he told PGA Tour Radio. "Threw it all out. It made a big difference. Just went with speed."
His putting performance was a reminder of his stirring finish at Royal Birkdale last month, where he went five-under over a four-hole stretch late in the final round to win the third major championship of the season.
Glen Oaks, with its deep rough and undulating greens, is more a U.S. Open-style course than a British links and joint leader Vegas handled it better than most, his five-birdie performance a continuation of the form that won the Canadian Open last month.
Vegas said his game had been transformed since he reverted to an old set of Mizuno irons that had been gathering dust.
"I’ve been driving the ball great all year but my irons hadn't been great," he said.
World number one Johnson had good cause to believe he should have the outright lead, after wayward drives at his 13th and 14th holes led to consecutive bogeys.
Fellow Americans Matt Kuchar (64) and Bubba Watson (68) are one shot behind the four-way tie for the lead, while first round co-leader Russell Henley is two back with Englishman Justin Rose and Spaniard Jon Rahm.
Defending FedExCup champion Rory McIlroy is seven strokes behind after a 68, while this season's points leader Hideki Matsuyama missed the cut by one stroke after three-putting the last for 69 and a three-over 143 score.
Matsuyama lipped out from four feet as the putting issues that cost him a chance of winning the PGA Championship two weeks ago continued.
(Reporting by Andrew Both in Cary, North Carolina, editing by Pritha Sarkar / Ian Ransom)
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