Johnson and Poulter took the lead with birdies on their first four holes and had no trouble the rest of the way in finishing at 30-under 186. Clarke and McDowell (59) never came closer than two strokes.
The two teams passed second-round co-leaders Jerry Kelly and Steve Stricker (64) and Fred Funk and Kenny Perry (66). Kelly and Stricker, the defending champions, tied for third at 26 under with Chris DiMarco and Anthony Kim (61).
The 12 teams in the tournament hosted by Greg Norman at Tiburon Golf Club played modified alternate shot in the first round and better ball in the second. Johnson and Poulter split $750,000 from the $3 million purse.
Johnson and Poulter, who played for the rival U.S. and European Ryder Cup teams two months ago, made the perfect duo in the three-format tournament.
After a birdie on No. 3, they maintained sole possession of the lead, although Clarke and McDowell gave chase.
"They kind of pushed us around," Poulter said. "You know what, making the birdies they did, it was kind of good for us to see good shot after good shot, and good putts going in. It's a lot easier to hole putts when your playing partners do."
Funk-Perry and Kelly-Stricker started the day in front by a shot, but both teams started slowly. Funk-Perry made a birdie, then eight straight pars. Kelly-Stricker had three birdies on the front.
With Johnson putting first in the scramble format, Poulter took advantage, perhaps nowhere more so than on the par-4 15th. Holding a two-shot lead, Poulter knocked his approach to 7 feet after Clarke had put his close. After Johnson missed his putt, Poulter made his to keep the two-shot advantage.
The two teams parred the par-3 16th, but with the par-5 17th ahead, Clarke and McDowell had another chance. They couldn't reach the green in two, but neither could Johnson and Poulter.
"It was definitely a lot harder than it looked," Johnson said. "Standing there we were like, 'Oh, this is a piece of cake."
Poulter came through, pitching to 7 feet. Then Johnson made the putt to follow Clarke and McDowell's birdie.
"Ian is one of the best chippers of the ball in the world, and he was the man for the job," McDowell said. "He was pretty clutch today. He played great."