The Masters champion had endured two frustrating days and was even in danger of missing the cut on Friday - creeping into the weekend on two-over-par after rounds of 74 and 70.
But with roars of "Rahmbo" ringing in his ears from the packed galleries, he caught fire to romp into second place midway through the afternoon on six-under-par, behind runaway second-round leader Brian Harman who was yet to start his third round.
"Yes, that's the best round I've played on a links golf course ever," Rahm, whose best Open finish was tied third in 2021, told reporters.
"The job today was to come out and give myself the best opportunity I could. Whenever you get a birdie, just thinking about one more. That's simply all you can do."
Rahm's charge took a while to get going as he parred the opening four holes on a morning when the wind of the previous two days was replaced by rainy conditions.
He rolled in a 10-foot birdie at the fifth and sunk one from 20 feet at the ninth.
But that was only a foretaste of what was to come. He birdied the 10th, 11th, 12th and 15th and then at the 16th drained a monster putt.
Just as the leaders were starting their rounds, Rahm then nailed another birdie on the 18th to send out a powerful message ahead of Sunday's conclusion.
Only one player has come from 12 or more shots back after 36 holes to win a major. That was George Duncan in the 1920 Open.
Rahm said a round like Saturday was what all the hard yards in practice are for.
"It feels really, really good," he said. "You visualise in your head and what you see is supposed to happen.
"You see everything the way it's supposed to happen unfold, and it's very unusual."
Rahm's 63 eclipsed any round that Spanish great Seve Ballesteros put together in his three Open triumphs.
"I'd rather win three times and never shoot 63, I hope that answers your question," he said when asked about the comparison with his famous compatriot.
