Johnson's birdies at Nos. 16 and 17 gave him a one-shot lead, with four other golfers within a single stroke.
In the end, it was Johnson who emerged on top, finishing at 9-under 271 at the TPC Southwind, earning his sixth career win and first since The Barclays last year.
Johnson now heads to Olympic Club as the favorite for next week's U.S. Open.
Third-round co-leader John Merrick registered a 2-under 68 to grab sole possession of second place at minus-8.