Johnson began the final round two strokes back and held a piece of the lead three different times. He won his sixth career title with consecutive birdies on Nos. 16 and 17 and finished 9-under 271.
He aggravated his back in early March lifting a jet ski at his home and didn't return to the PGA Tour until last week at the Memorial, where he tied for 19th.
Johnson, who picked up the $1.008 million check, led by only a stroke going to No. 18. Rory McIlroy, Chad Campbell and Nick O'Hern, three of the four who had a chance to tie Johnson with a birdie, knocked their tee shots into the lake.