Johnson played the last six holes in five under par at Sheshan International Golf Club to card a closing 66 and finish 24 under par, three ahead of defending champion Ian Poulter.
All three members of the final group of Johnson, Poulter and Graeme McDowell shot 66, meaning Poulter finished one ahead of Ryder Cup team-mate McDowell, with Spain's Sergio Garcia two shots behind in fourth after a closing 63.
US Open champion Justin Rose was fifth on 16 under and Rory McIlroy's share of sixth with Canada's Graham DeLaet on 15 under was more than enough to secure the former world number one's place in the season-ending DP World Tour Championship in Dubai.
"I didn't get off to the best start and Poulter and McDowell got off to great starts and put a lot of pressure on me, but I am swinging well and putting well so thought just stick to my game plan and play the golf course how I want to play it and it's going to come," Johnson said after claiming his eighth PGA Tour title and the first prize of just over one million euros (£856,000).
"I played really well the last few holes on the front nine and then had a great back nine. The guys made it really interesting but I just played really well coming down the stretch. They put a lot of pressure on me but I am really proud of myself and the way I handled it."
Johnson has not always handled such pressure so well, McDowell famously winning the 2010 US Open at Pebble Beach after Johnson squandered a three-shot lead in the final round. After a triple-bogey on the second hole and double-bogey on the third, Johnson shot a closing 82 and McDowell's 74 was enough to win by one from France's Gregory Havret.
"It takes a while to learn that (maturity and patience)," added Johnson, who also missed out on a play-off for the 2011 US PGA Championship after receiving a two-shot penalty on the 72nd hole for grounding his club in a bunker.
"I wish I would have had some of that a few times a few years ago, but you learn from your mistakes and try to get better from them and I think I showed a lot of patience and a lot of discipline with clubs I picked and shot selection.
"This is the biggest win of my career and hopefully there are better things to come. A major is always the next step. Am I suited best for one or the other? I don't think so. I think they all suit me very well.
"If I play like I did this week, I'm going to win one for sure. I grew up right down the street from Augusta (venue for the US Masters), so that would be my favourite one. I just love playing that golf course."
Johnson began the final round three shots clear of Poulter but three-putted the opening hole as the Englishman birdied the first and second, while McDowell joined Poulter in the lead with birdies at the first three holes.
Birdies on the eighth and ninth got Johnson back into a share of the lead and although Poulter edged in front with a birdie on the 12th, Johnson birdied the 13th and matched Poulter's birdie on the 14th to set up a grandstand finish.
Johnson was left alone in the lead when Poulter was unable to get up and down from a greenside bunker on the 15th, although with the 16th being a reachable par four and the par-five 18th still to come - Johnson took seven there on Saturday - the result was far from settled.
None of the final group tried to drive the green on the 16th, although Johnson's length meant he could hit a long iron just 10 yards short and he promptly chipped in for an eagle two.
Poulter's birdie left him two behind and the gap was three when Johnson hit a superb tee shot to eight feet on the 17th and holed the birdie putt.
"I guess it was a good defence," Poulter said. "Obviously I'm a little disappointed not to put my hands back on the trophy, but 15 birdies and an eagle at the weekend is some pretty good golf. So it's exciting for the next few weeks ahead and obviously it's some good points on the board obviously for Ryder Cup (qualification) and the Race to Dubai.
"I'm in great form. I really am playing well. The work I've done leading up to this run of tournaments has really worked and I couldn't be hitting it any better right now and obviously rolling a few putts in."
Despite a flawless final round McDowell was also disappointed, the Northern Irishman not dropping a single shot over the weekend as he closed the gap on Henrik Stenson at the top of the Race to Dubai to just over 145,000 points.
"Obviously there is a pang of disappointment, but generally just very proud of myself the way I played this week, tee to green especially," McDowell said. "On the greens, room for improvement.
"But I didn't make a bogey all weekend. I shot 14 under on the weekend. Dustin Johnson was in a different league off the tee and gave us a little bit of a sniff and then promptly slammed the door."