Morikawa and Spaun were both in the clubhouse at Kapalua on nine-under par 64 when Rahm birdied three of his last four holes to join them.
Morikawa had raced up the leaderboard with six straight birdies from the 10th through the 15th.
He finished with nine birdies in all, as did Spaun, who strung together four in a row at the 12th, 13th, 14th and 15th.
Rahm followed a birdie bomb at the fourth hole with a 19-foot eagle putt at the fifth.
He was two shots off the lead after birdies at the sixth, eighth, 10th and 12th when he bogeyed the 14th - where he was unable to get up and down from a greenside bunker.
He responded with a four-foot birdie putt at the 15th, a seven-foot birdie at 16 and a two-putt birdie at the 18th for his share of the lead.
"I made a lot of good swings out there," Rahm said, but added he thought his best shot of the day was a 20-foot birdie putt at the 10th.
"After somehow leaving a six-footer short and not hitting my best shots on nine, to come back and make that 20-footer was a big thing," he said.
Rahm came up a shot behind last year's tournament winner Cameron Smith, who finished with the lowest 72-hole tournament score in US PGA Tour history with a 34-under total.
Despite his own scorching week last year, Rahm said he couldn't say the Plantation Course owed him one.
"I shot 33-under. I got beat by 34-under," he said. "That's just what it is. It was a great battle. If we get to that point again, hopefully it's me and hopefully I end up winning by one."
Morikawa, winner of the 2020 PGA Championship and the 2021 Open Championship, has slipped to 11th in the world after a largely unrewarding 2022.
However, he said recent work on various parts of his game with specialist coaches was paying dividends, particularly with his putting.
"Speed control was a big one," he said of his improvements on the greens. "I think today I did a pretty good part on that, just kind of dripping them in - having really good speed. I think I had one or two putts that were just a little off."
He got his round going with a 25-foot birdie putt at the fourth.
"That just kind of got the round propelled from there," said Morikawa, who drained a 20-footer for birdie at the 11th.
Spaun also played without a bogey.
"I drove it nice. I putted nice, so I really can't complain about anything today," he said.
The leading trio were a stroke in front of rising South Korean star Kim Joo-hyung, who shook off an early bogey to card an eight-under par 65 that featured two eagles.
The first was a hole-out from the fairway at the par-five sixth, the second a five-foot eagle putt at the par-five 15th.
