Scheffler, this year's Players Championship winner, began the day on 10-under par at East Lake in Atlanta with a two-stroke lead over Norway's Viktor Hovland thanks to staggered scoring based upon season point totals.
But the American was undone by a triple bogey at the par-3 15th, finding water off the tee and needing three putts to finish, as his season points edge evaporated after he fired an opening 71.
Morikawa, who began on 1-under and nine adrift of Scheffler, fired the lowest first round in Tour Championship history, making seven birdies and an eagle on a bogey-free day.
"I've grinded my butt off. I've spent way too much time out there," Morikawa said. "But I figured some things out. It's obviously nice to see."
Due to the odd scoring format, Morikawa was on 10-under and sharing the lead with fellow American Keegan Bradley, who opened with a 63, and Hovland, who shot 68, with Scheffler fourth on 9-under after firing 71.
"Im pretty frustrated with how I played," Scheffler said. "I guess it's a little bit of a blessing to have a pretty bad day and still be in the tournament. So go out there tomorrow and just keep fighting."
The 61 was Morikawa's career-low PGA Tour round, one under his final round at last year's Tournament of Champions, and one off the course record 60 fired by Zach Johnson in 2007.
Defending champion McIlroy, the world number two and four-time major winner from Northern Ireland, struggled through back pain with a 70 to finish three off the pace, exactly where he began the day.
McIlroy suffered the injury while exercising at home on Tuesday and had no practice before his round.
"My whole lower back spasmed, seized up. I couldn't move," McIlroy said. "I honestly couldn't address the ball this time yesterday. So to get to where I am today is good."
McIlroy was 2-over on the day after 11 holes and eight adrift but made three birdies in four holes and with Scheffler's fade not even a closing bogey could dim his fightback.
"I hung in there and I just felt like if I could get through today, it's better than it was yesterday, hopefully tomorrow's better than it was today, and just sort of try to keep progressing," McIlroy said.
The 30-player fight for an $18 million FedEx Cup season points playoff top prize tightened greatly with Morikawa stealing the show.
"You've got to have your foot on the pedal," Morikawa said. "This is the end of our season for a reason. Even though I had a great round today I want to keep doing that for next few.
"I haven't been this pin-high with my irons in quite some time. That's a sign of control. And then being able to make some putts. I still left some out there but I'm not going to complain at all. I'm very, very pleased with this round."
- 'One of those days' -
Bradley, who began seven off the lead, was thrilled as well after birdies on three of the last four holes to finish a bogey-free round.
"It was one of those days where everything was going right," Bradley said. "I made a bunch of putts, I hit the ball great and when I missed some shots I hit them in great spots and got them up and in."
Bradley said it was crucial to make the move early to make up his deficit quickly.
"It was so important," he said. "When you get here everything sort of amplifies so I'm proud."
Morikawa, whose last win came at the 2021 DP World Tour Championship in Dubai, sank a three-foot birdie putt at the first, a 20-foot birdie putt at the fifth then eagled the par-5 sixth after dropping his second shot inside four feet from the hole.
He added a 12-foot birdie putt at 10, a 36-foot birdie putt at the 12th, a 10-footer to birdie 16, a 13-foot birdie putt at the 17th and a six-footer at 18.
