The five-time major winner was left frustrated after Team USA squandered a lead twice in the closing holes of their fourball match against Rahm and rookie Nicolai Hojgaard.
Rahm chipped in for eagle on the 16th to square the match and then made another eagle on the 18th after bumping a putt off the backboard before the ball bounced up and nestled into the hole.
It means Europe cemented a commanding lead 6.5 to 1.5 after day one, with Koepka upset at his side’s performance and the score.
“I mean, I think me and Scottie birdied, what did we say, 14, we birdied 14, 15, 16, 17, 18, and then lost by two,” Koepka said after the tied match.
“So yeah. I mean, I want to hit a board and pout just like Jon Rahm did. But, you know, it is what it is. Act like a child. But we’re adults. We move on.”
Pushed on Koepka’s comments, Europe captain Luke Donald played down any issue over Rahm’s behaviour.
"I didn't see any of that,” Donald said. “Jon was a big support system for Nicolai, to hit a drive like that on 18 and make an eagle for a half, he's a passionate person, I didn't see him acting any other way."
While Zach Johnson sympathised with Koepka’s frustration: “I'm sure Brooks is frustrated, like all 12, 18 of us, with today and the result.
“The way I see it, they were one down, the only thing you can't do in that situation is leave it short? Played the percentages, tip of the cap. Well done.”
Rahm is yet to respond, although the Spaniard will likely be asked about Koepka’s criticism on day two.
The prospect of the pair facing off in a Sunday singles match is tantalising, with Rahm already playing a vital role in Europe’s quest to reclaim the Ryder Cup.
Rahm had earlier combined with Tyrrell Hatton for a dominant 4&3 foursomes victory over Scheffler and Sam Burns.
Moments after Rahm’s heroics, Matt Fitzpatrick claimed his first Ryder Cup point after five straight losses, the former US Open champion making four birdies and an eagle in the first six holes to set himself and Rory McIlroy on the way to a 5&3 win over Collin Morikawa and Xander Schauffele.
Max Homa and US Open champion Wyndham Clark looked set to claim a first win for the visitors when they won the 16th to go two up on Justin Rose and Robert MacIntyre, but Rose’s par was enough to win the 17th and the Englishman then birdied the last to cap a stunning finish. It means Luke Donald’s side hold a commanding lead heading into Saturday morning’s foursomes.