The American duo, who have six majors between them, went toe-to-toe at the Austin Country Club before Johnson emerged victorious thanks to impressive putting in the closing holes.

Koepka established an early 2-up lead thanks to back-to-back birdies but Johnson continued to pressurise his opponent.

The match turned when Johnson landed a 27-foot birdie on the par-four 15th hole as Koepka missed his 24-footer.

Johnson saved a tough par on the 16th hole before sealing a comeback victory with an eagle on the last.

The 37-year-old, who last triumphed in the event in 2017, moves through to the semi-finals where he will meet compatriot Scottie Scheffler.

Scheffler is the highest seed left in the draw at number five and can become world number one with victory in Texas.

Ireland’s Seamus Power battled hard as he drew level going into the back nine but Scheffler came out on top with a 3 and 2 win.

"I've been watching [Johnson] play for years now, and he's pretty good at golf," said Scheffler.

"So it should be a fun battle with him tomorrow.

"It's good to see him back in form again, and I look forward to battling it out with him."

The other semi-final will see Kevin Kisner of the US and Canada’s Corey Conners go head-to-head at the Austin Country Club.

Kisner was in superb form as he stormed into a 3-up lead through four holes courtesy of three pars and a birdie against American Will Zalatoris before increasing his advantage with a birdie on the par-three 11th.

Zalatoris kept his hopes alive with a 27-footer for par on the 14th hole but needing to win the next four holes to force a playoff, the American was unable to chip in for a birdie at the par-four 15th as Kisner secured a comfortable win.

Conners and Mexican Abraham Ancer traded two birdies each over the first 11 holes before the former found an extra gear.

The Canadian struck birdies at the 14th and 16th holes before holding on to clinch a 2-up victory to progress to the semi-finals.

"It feels great to be sitting here," said Conners.

"I think I'll have some adrenaline tomorrow, and that will help get me through."

All the last 16 matches were played earlier today, with Conners defeating Japan’s Takumi Kanaya by 5 and 3.

Ancer beat world number two Collin Morikawa of the US by 7 and 6 and Zalatoris needed a fourth extra hole to overcome American Kevin Na.

Kisner came from behind to defeat Australia’s Adam Scott, Koepka edged world number one Jon Rahm of Spain and Johnson beat England’s Richard Bland by 3 and 2.

In the other last-16 matches, Power claimed a 4 and 3 win over Englishman Tyrrell Hatton, while Scheffler knocked out defending champion Billy Horschel of the US.

Competition is set to conclude tomorrow with the semi-finals and final.