The following match was equally tight, with Rahm and Nicolai Hojgaard pegged back from two up after eight to all square by world number one Scottie Scheffler with wins on holes 10 and 11.
Brooks Koepka edged the Americans in front with a birdie on 15, but Rahm holed his second chip-in of the day to win the par-four 16th with an eagle.
The Spaniard’s wild celebrations were matched by an unusually animated Scheffler after he won the 17th to put the Americans one up with one to play and guarantee at least another half point.
A half point is all they would get though after Rahm produced another eagle to win the 18th, ramming a 33-footer into the hole at pace.
“There was definitely a bit of Seve magic on that one,” said Rahm, referring to the late Seve Ballesteros, who has a space dedicated to him in the European team’s dressing room.
“He definitely pulled that one towards the hole.”
Koepka, meanwhile, complained about Rahm’s behaviour on the course, saying: “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.”
It is not clear what the Spaniard did, or on which hole, to attract the ire of his opponent.
That left one match out on the course, with Rose – partnered by Scotland’s Bob MacIntyre – at his grinding best, refusing to allow Americans Max Homa and Wyndham Clark breathing space.
Three times he won a hole on the back nine to reduce the deficit to one.
The final time was with a par on the 17th to send the match down the 18th and Rose nailed an eight-footer, before beating his chest in a fashion reminiscent of Ian Poulter, as he gave Europe a five-point lead after day one.