– Rory McIlory walked past Tiger Woods on the practice range at Augusta National Golf Club, shook his head in mock shock and said, “I never thought I would see the day — Tiger and Phil playing a practice round together.’’

Woods and Mickelson, the Amazon and Apple of American golf, hadn’t since 1998. Now both in their 40s, with Woods returning to the Masters after a series of back surgeries, they turned a meaningless Tuesday morning into an homage to their best Sunday afternoons, replete with massive galleries and echoing roars.

On the 15th hole, Woods blasted a driver past his partners, hit a midiron to 4 feet and made eagle. Mickelson birdied, then they moved behind the green to practice flop shots.

Mickelson launched a ball almost straight into the air. When it landed softly and trickled into the hole from 40 feet away, he bumped fists with ... Woods?

This is detente on bent grass, Coke and Pepsi sharing a glass. The often unfriendly rivals weren’t merely practicing together — they had formed a team, winning a money match against Fred Couples and Thomas Pieters. “We got shillelaghed,’’ Couples said.

Woods-Mickelson is the dynamited duo who, when paired at the Oakland Hills Ryder Cup by American captain Hal Sutton, barely spoke to each other while losing two matches and precipitating a European romp. Their newfound affection is rooted in Woods’ newfound humility and their recent visit to Chaska.

Woods, sidelined because of his back, became a U.S. vice captain at the Ryder Cup at Hazeltine National, and Mickelson became the most vocal leader for a team that won in a rout.

“We have been through it for so long and we have been together on these teams long enough,’’ Woods said. “Then when I got hurt and had to take a different role on the teams ... Phil was great. He was trying to help me out when I was trying to make a comeback.

“Our friendship has certainly gotten a lot better. I think it’s age, as well. We’re at the tail end of our careers, we both know that. He’s 47, I believe, and I’m 42, and we have had a great 20-year battle. Hopefully, we’ll have a few more.’’

They may be the two most fascinating golfers of their generation, and their performances at the Masters helped jump-start and define their careers. To see them bumping fists on the 15th hole on a Tuesday morning is almost too much to ask for, which is why a massive gallery followed them around, packing the area around the 18th green as if one of them was about to win another green jacket.

Woods announced his arrival on the world stage by winning his first Masters in 1997 by 12 strokes, then won three more by 2005. Mickelson finally won his first major at Augusta National in 2004 and with a victory this week would earn his fourth green jacket, tying Woods and Arnold Palmer for second most, two behind Jack Nicklaus.

Two players in Masters history, according to the Golf Channel’s Justin Ray, have played at least 25 rounds with a scoring average better than 71.5: Woods and Mickelson.

Both have played well lately, and both played well over nine holes Tuesday, with Woods shooting 5 under par from holes 13-16.

“Nobody respects and appreciates what he’s done for the game more because nobody’s benefited from what he’s done for the game of golf more than I have,’’ Mickelson said. “To see him back out playing is incredible. We all feel that.

“I texted him a while ago when he was playing at Valspar that it felt like it was a different time continuum because I found myself pulling so hard for him.’’

During his prime, Woods treated interviews as annoyances. He treated Tuesday’s as if it was group therapy.

He’s dealt with scandal, injury, reinjury and athletic mortality. Whether he’s genuinely humbled or whether humility is merely his club of choice this week, Woods sounded uncommonly human. He hasn’t played at the Masters since 2015. When was the last time he felt so healthy? “It’s been probably seven, eight, years,’’ he said.

At last year’s Champions Dinner, he had trouble sitting still because of shooting pains in his back and leg. He admitted to falling down because his leg wouldn’t function.

With an intense yet cautious rehabilitation that has included swimming, core exercises and less time on the range than in his prime, he has regained his prodigious length, saying his swing speeds are reaching 129 miles per hour despite his recent back fusion surgery.

“It’s crazy,’’ he said. “I thought prior to the surgery, ‘That’s pretty much it. I’ll have a nice, comfortable and great life, but I’ll never be able to swing the club like I used to.’ ”

Woods felt good enough about his game and his relationship with Mickelson to bring out, as he calls it, “the needle.’’ Tuesday, Woods wore a sleek, collarless shirt from his collection, Mickelson a baggy, long-sleeve that looked like something John Daly would throw away.

“I always give him a little bit of grief about that,’’ Woods said. “The only thing that was missing was a tie.’’

“I have a tie,’’ Mickelson shot back. “I’m wearing it tonight.’’

Meaning: at the Champions Dinner.

There are comebacks, and then there are comebacks.

Jim Souhan’s podcast can be heard at MNSPN.com.

On Twitter: @SouhanStrib

E-mail: jsouhan@startribune.com.