The tight leaderboard featured six others at three-under on 68. Swede Jonas Blixt, Americans Jason Dufner, Kevin Na, Luke List, Brian Harman and Grayson Murray all were within striking distance.
Johnson is finally showing the form he displayed before injuring his back while falling down stairs on the eve of the Masters in April.
"When you win, you're playing well, so it gives you a lot of confidence," he told PGATOUR.com.
"For me, that was one thing that was probably lacking a little bit the last few months – just the confidence, just because I wasn't seeing the shots that I wanted to see.
"I wasn't hitting them consistently. So the confidence was just down a little bit.
"But you know, after last week, obviously I've got a lot of confidence now. I feel like the things I've been working on, they are back to working."
Johnson started on the back nine and used a superb approach from 221 yards to set up a four-foot putt for eagle on the par-five 18th hole to reach the turn in four-under 31.
The long-hitting American, who leads the FedExCup standings, mixed a bogey with two birdies over his next four holes before a steady finish.
British Open champion Spieth, who held a five-shot lead in the final round last week, bogeyed three of his opening seven holes but used birdies at his 13th and 16th holes to get to one-over-par 72.
Defending champion Rory McIlroy also was at 72 after a birdie at the 18th hole. McIlroy's up-and-down round included three birdies, two bogeys and a double bogey at the par-three 11th.
This week's field features the top 100 players in the standings. The top 70 after Monday's final round advance to the penultimate event to be played Sept. 14-17 at Conway Farms in Lake Forest, Illinois.
(Reporting by Frank Pingue in Toronto and Gene Cherry, editing by Gene Cherry/Greg Stutchbury)
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