While Johnson, who had been dominant this week at Austin Country Club, endured his closest match of the week, defeating Hideto Tanihara, 1 up, with clutch putts at Nos.
Rahm beat American Bill Haas 3&2 in their semi-final and will become the youngest ever victor of a WGC event if he can overcome Johnson in the 18-hole final.
Fisher managed to extend the match with back-to-back birdies at 14 and 15, but the game was up at the next as he was safe in the knowledge that he would be returning to Augusta National for the first time since 2012.
"I try to stay humble", Rahm said.
"Against Phil, I really felt like I needed to capitalise when I had the chances, and I was able to do that", Haas said.
Throw in the fact that players on the fringe of the Top 50 are attempting to qualify for the Masters in a couple weeks, and this is some high-stakes golf. "My goal was to get to the Masters". McIlroy won't change his plan to skip the Houston Open just to get in some extra play.
For the first time during the WGC-Dell Technologies Match Play tournament, Dustin Johnson was tested.
"He hits the ball a long way", Haas said. "He's certainly going to be very hard".
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The American had led 3-up after seven holes but Tanihara made four birdies in the next seven holes to level the match.
Haas' round of 16 match against Kevin Na came down to the 18th hole, where Haas won 1 up.
Rahm will take on Charles Howell III, who won a sudden-death play-off against Rafa Cabrera Bello and Tyrrell Hatton on the fifth hole with a birdie from four feet to advance as the Group 10 victor. And yet, Noren gave him a terrific battle having clawed back a three-hole deficit to sit all square on the 13th tee.
Three-time Masters victor Mickelson had not trailed this week until Haas opened their match with a birdie. 17 (6 ½ feet) and 18 (8 feet). "Obviously, representing Spain, we want as many Spaniards to make it as far as possible", Rahm said.
"Towards the end, especially, I really made a couple of clutch putts".
Rahm's hot play shouldn't surprise anyone; he won his first career PGA Tour event at the Farmers Insurance Open in January and almost won the WGC Mexico Championship, where he finished third earlier this month.
On playing his idol Sergio Garcia, who the younger Spaniard has watched play golf for years, Rahm said: "I've been following his career forever, he's a great role model of mine".