The American began the day in a four-way tie for the lead and recovered from a bogey on the first with his fifth birdie of the day on the 10th.
Spieth carded three more in succession from the 14th to finish 12 under par, three shots ahead of Dustin Johnson.
"I've been striking the ball well this year," the 24-year-old said.
The three-time major winner, who also pulled off an impressive shot from eight feet to three-putt the ninth, had been four clear until world number one Johnson birdied the 18th to complete a 67 and move two ahead of Paul Casey, Jon Rahm, Patrick Reed and Matt Kuchar.
Spieth, who has won each of the five times he has enjoyed a lead of two shots or more after 54 holes on the PGA Tour, felt a "heated putter" had been crucial to his success.
"Today was about the most committed I've been finishing a round - Michael [Greller, his caddie]said ever - and I agreed with him," he added.
"[We] committed to targets that were away from holes, knowing I'm in the lead and knowing the putter is getting hotter each putt I hit. That last six-hole stretch, I played beautiful golf."
Open champion Jordan Spieth edged closer towards his fourth win of the season after a six-under-par third round of 64 in the Northern Trust.