Johnson became the first player to have won all four World Golf Championship events by beating Rahm by one hole in a dramatic final at Austin Country Club.
The 32-year-old never trailed at any point in his seven matches and was only taken beyond the 16th hole for the first time in a hard-fought semi-final victory over Japan's Hideto Tanihara.
But he was also made to work hard to secure the first prize of £1.3m in the final as Rahm, who was trying to become the youngest winner of a WGC event, fought back from five down after eight holes to take the contest to the 18th.
Rahm missed good birdie chances on the first two holes and fell behind with a bogey on the third after finding thick rough off the tee, before compounding that mistake by three-putting the next.
It looked as though the 22-year-old would escape with a half on the short fifth after his chip from the side of the green hit the pin, but he missed from four feet after conceding Johnson's birdie putt.
Another birdie on the sixth extended Johnson's lead and it would have been even bigger but for Rahm holing from 25 feet for par on the seventh after hitting his long birdie putt off the green.
However, Rahm's frustration was mounting rapidly and he kicked his driver along the ground in frustration after a wayward drive on the next led to another loss and a five-hole deficit.
Rahm, who beat American Bill Haas 3&2 in their semi-final, was handed a lifeline when Johnson bogeyed the ninth and 10th, and although the US Open champion bounced back to birdie the par-five 12th, Rahm drove the green on the short 13th and two-putted for his first birdie of the day.
A birdie on the 15th was followed by a remarkable one on the 16th, Rahm hitting his second shot seemingly straight through a tree before holing from 30 feet to get back to just one down.
Extra holes looked on the cards when Rahm drove to the back edge of the 18th green, but a terrible chip took the pressure off Johnson and he safely made par from the fringe to secure the title.
Johnson and Tiger Woods are the only players with five or more WGC titles and although Woods won an incredible 18, the former world number one failed to collect the HSBC Champions trophy in his only two appearances.
Haas beat Tanihara 2&1 in the play-off for third place, although Tanihara had the thrill of making a hole-in-one on the seventh.
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