Johnson carded a closing 66 to finish at 24-under-par 264 at Sheshan International with Poulter also shooting 66 for second place on 21-under. Northern Irishman Graeme McDowell was another shot back in third after also carding 66.
Johnson, 29, collected $1.53 million for his first victory in a World Golf Championships event and eighth on the PGA Tour.
He started the final round with a three-shot lead over Poulter but surrendered it after only two holes only to come on strong on the back nine.
"I knew if I stuck to my game plan it would come," Johnson said. "I was swinging well and putting well."