Rahm and Palmer played 30 holes Saturday in the event delayed by rain for more than seven hours Thursday, finishing off a 7-under 65 in the alternate-shot second round and shooting 64 in best-ball play in the third.
"It's been 4:30 four nights in a row," Palmer said. "Dinners at 9 and back up at 4:30. Took its toll on me. Just feeding me sugar and food trying to keep my energy up. Tomorrow we'll be on a lot of rest. If we're on tomorrow in alternate shot, we're going to be hard to beat."
Rahm carried the team in the third round, making eight birdies.
"He's just fun to be around," Palmer said. "He's actually a great guy. I've enjoyed every second with him. When you're up close and personal and watching it and see the shots he can hit around the green, you know, his short game is phenomenal. You can learn something from that, too, so I learned a lot. Honor to be a part of it."
Palmer saved bogey with an 8-footer on the par-3 17th after both players hit into the water, and Rahm made a 15-foot birdie putt on the par-5 18th to match Stallings and Mullinax at 23-under 193.
"That putt Ryan made was probably the most important shot we made so far in the tournament," Rahm said. "Felt like a birdie, and then to keep tied for the lead, very important."
Stallings and Mullinax played 27 holes, shooting 70-62.
"We play a lot of practice rounds together," Stallings said. "We've known each other for a few years. Just kind of we played so much together it just kind of made sense. We know each other's games pretty well."
Mullinax looked ahead to the final round.
"I really enjoy alternate shot," Mullinax said. "Scott hits the ball great. Hitting it nice. We're both putting well. I don't feel like there is much pressure on us. Just go out and do our thing."
"I think we played 50-odd holes," Harding joked. "We certainly moved up the board. It's just a matter of continuing the momentum throughout the rounds."
Sergio Garcia and Tommy Fleetwood were another stroke back with the teams of Joel Dahmen-Brandon Harkins, Austin Cook-Andrew Landry, Hank Lebioda-Curtis Luck, Russell Henley-Ryan Blaum and Russell Knox-Brian Stuard. Brothers Brooks and Chase Koepka topped the group at 18 under along with Henrik Stenson and Graeme McDowell.