From five down through eight holes, Rahm somehow took the hottest player on the planet to the 18th hole where, had it not been for an unfortunately timed noise in his backswing, he may well have pushed Johnson to extra holes.
What promised to be an epic final at the Austin Country Club in Texas didn’t live up to its billing on the front nine but turned into an enthralling battle over the closing stages courtesy of some explosive play by Rahm.
After halving the first two holes, Johnson did what he had done all week and raced to a big lead before the players hit the turn.
As Rahm battled his swing, the American reeled off five wins in six holes and stood on the ninth tee in a commanding position.
But the former standout amateur, who Phil Mickelson has tagged as one of the biggest future stars of the game, began a courageous fightback at the ninth where he cut the deficit to four holes with a par.
More problems for Johnson at the 10th led to a second straight bogey and Rahm capitalised to make the difference three, where it remained as both players parred the par-three 11th.
At the par-five 12th, Rahm hit first and ripped his tee shot just shy of 400 metres at the downhill, downwind hole then Johnson followed with a drive that was just 10 metres shorter.
Both players hit wedges for their second shots to the 530-metre hole but it was Johnson who converted for birdie while Rahm missed a short putt for the halve to go to the driveable par-four 13th four down again.
After Johnson stuck to his game plan and laid up off the tee with an iron, Rahm hit a remarkably courageous shot, smashing driver straight at the flag across the water and dropping the ball some 20 feet behind the hole.
Johnson’s wedge didn’t finish close enough to convert for a birdie while Rahm took two putts and, with five holes to play, the difference was three.
Both players made orthodox pars at the 14th, then Rahm hit an exquisite sand wedge to three feet at the 15th while Johnson’s second finished 10 feet away.
When he missed the birdie putt, Rahm found himself just two down with thee to play and there was a sense the momentum was in his favour.
At the par-five 16th, both players hit terrible tee shots way right of the fairway but Rahm’s ball found a horrible spot behind some trees in deep rough.
It looked as though his charge may have come to an end, and after Johnson laid up within 50 metres of the green, Rahm was confronted with what looked to be the crucial moment of the match.
Faced with the choice of wedging over the trees in front and leaving a long third or taking the high risk option of punching underneath with a long iron, he took the latter and, thanks to a little bit of luck, pulled off a remarkable recovery.
But such heroics are of little value if the player doesn’t capitalise and Rahm once again proved himself capable in the biggest moments by getting up and down, with a 30-foot putt, for a winning birdie.
Having cut the margin to just one with two to play, the youngster miscued again at the short par-3 17th but saved the situation courtesy of a deft pitch between two sprinkler heads for a par and the half.
With the honour on the 18th tee, Rahm again showed bravado by pulling driver at the 350-metre par-four and blasting directly at the green.
His shot was almost perfect, coming to rest just behind the putting surface and giving him the opportunity to extend the match if he could find just one more bit of magic.
After Johnson’s approach came up short, Rahm set himself for a brutally difficult downhill chip and, just as he pulled the club back, there was a loud bang just to the right of the green.
The shot came up well short and left a treacherous putt and Rahm was clearly frustrated as he looked towards the source of the sound.
Johnson two-putted for the par and a 1up win but it had been an enthralling encounter which has only strengthened Rahm's claims to being one of the most exciting prospects in the game.
Johnson admitted afterwards he had been pushed hard by the rookie.
“I didn’t really give him any holes except for 10,” he told Golf Channel’s Steve Sands immediately after the win.
“I three-putted 10 but it was tough out there. The greens got really fast and the wind was affecting all the putts.
“But Jon played really well. I really didn’t give him anything.”
Johnson had also been pushed in his semi-final match against Japan’s Hideto Tanihara where he also squeezed out a 1up victory with a par at the 18th.
Tanihara went on to lose the consolation match 2&1 to Bill Haas though did make the highlight reel with a hole-in-one at the par-3 seventh.
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