The result guarantees him a first top five finish anywhere in the world since he won the Saudi International in February last year and, regardless of what happens on Sunday, provides him impetus heading into next month's first Major of the year at Augusta National.
Koepka had taken early control of the match with winning birdies at the second and third, the first of them from off the green.
The pair exchanged holes in messy fashion before and after the turn which brought the game back to stalemate.
Johnson finally got his nose in front with a birdie from 27-feet at the 15th and he confirmed the win by driving the green on the par-4 18th hole, a blow of 353-yards to 46-feet.
"I'm striking it really well, so I'm giving myself a lot of chances," Johnson explained.
"I'm playing really good golf. Didn't hole a lot of putts, especially today, but the conditions got tough this afternoon.
"The speed on the greens is tough to judge sometimes because uphill they're rolling at 10 and downhill they're rolling at 25. It's hard to judge."
A winner at Austin in 2017, he added: "I like this golf course. If you're hitting good shots, then you can shoot some good scores and I like the way I'm hitting the ball right now.
"I feel like I'm controlling the golf ball pretty well. That's what you've got to do in match play."
The result left him with an Austin Country Club record of 17-8-1, sufficient to make him favourite heading into the semi-finals where he will meet Scottie Scheffler.
The Texas resident has rubber-stamped both his 2022 form and his fondness for the course and format.
Last year's runner-up had exacted revenge on the man who beat him in the final 12 months ago, Billy Horschel, in the Round of 16, winning 1-up in a match that never had more than one hole in it, although it was also a little scrappy.
Scheffler turned up the heat in the afternoon to down Irishman Seamus Power 3&2.
He made birdie-eagle at the 5th and 6th to go 2-up before a bogey at the 8th and Power's par-breaker at the 9th drew the game all square at the turn.
But Scheffler made birdies at the 12th and 13th to re-establish his 2-up lead and a chip-in eagle-3 at the 16th sent him into Sunday's semi finals.
"I didn't have my best stuff this morning, but I hung in there and I played really good this afternoon," he admitted. "I didn't really give Seamus many openings."
Of his match play expertise and killer instinct he said: "I definitely get nervous. I think if you don't get nervous out here, there's probably something a little bit off with you. You probably don't care that much. I play better with a little bit of nerves."
And of the prospect of a head-to-head with Johnson he added: "I'm not going to do any research on DJ. I've been watching him play for years now and he's pretty good at golf.
"It should be a fun battle with him tomorrow. It's good to see him back in form again and I'm looking forward to battling it out with him."
The second semi-final will see 2019 tournament winner Kevin Kisner take on Canada's Corey Conners.
Kisner will be making his third appearance in the final four at Austin after defeating Will Zalatoris 4&3 in the last eight, while Conners overcame Mexico's Abraham Ancer on the final green.
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