Rose then produced five birdies in a stunning back nine of 31 to get to 14 under after a 67, with Johnson slumping to a closing 77.
The World Number One finished in a tie for second at 12 under alongside Swede Henrik Stenson and reigning US Open champion Brooks Koepka.
The victory was Rose's second World Golf Championships title after the 2012 WGC-Cadillac Championship and his first win since claiming gold at last year's Olympic Men's Golf Competition."This is really, really satisfying," he said. "All players pride themselves on winning and I've won every year since 2010 (worldwide). I was very aware that that was slipping away from me this year.