Stallings, who has missed the cut in his last six tournaments, fired a sizzling six-under-par 66 to grab a one-shot lead in the first round while Levin enjoyed one of the best putting days of his life to open with a 67.
While Stallings won his maiden US PGA Tour title in his rookie season at last year's Greenbrier Classic, he has been hampered by a lingering rib injury for much of his 2012 campaign.
"January 18th, I tore cartilage in five of my ribs and didn't know it was torn at the time," Stallings told reporters after taking control of the Jack Nicklaus-hosted tournament with three birdies in his last four holes.
"I played a few more events and was miserable. It was hurting every swing."
Stallings had an MRI scan which revealed the torn cartilage and he spent the next six weeks dealing with that.
"Then to try to grind through the Masters and get through on painkillers and stuff like that," he said of his eventual tie for 27th in the opening Major of the year.
"Somehow I played halfway decent, but it's been kind of a struggle getting through that. I wasn't able to work out, wasn't able to do the things you need to do to play against the best players in the world.
"But now I'm cleared and happy to be able to play injury free. I stayed positive throughout being injured. I kept telling myself that it was only a matter of time before a round like this was coming around."
Stalling snatched the outright lead from Levin late in the day at Muirfield Village Golf Club, his compatriot having charged to the top with six birdies, one bogey, a double-bogey at the 16th and an eagle at the seventh.
"It was a good day," said Levin, who has yet to win on the US PGA Tour. "I doubled 16, hit it in the water, but after that I kept my head together.
"From about (hole) three on, I was one putting pretty much every hole after that. I birdied three to go two under, and I made everything from there on in."
Levin totalled only 21 putts, and was delighted to regain good form for the first time in three months.
"I haven't been playing well ... and I still don't feel like I'm hitting it that great," the 27-year-old said. "Sometimes you need rounds like this to turn it around. Hopefully I'll keep it going."
Levin's best finish on the US PGA Tour was a playoff loss to Johnson Wagner at last year's Mayakoba Golf Classic but his most painful was a third place at the Phoenix Open in February when he briefly led by seven shots early in the final round.
"I still think about it from time to time, but it's not an issue when I've been playing," Levin said of his heart-breaking collapse in Phoenix where he closed with a 75.
"I'd like to be in that situation again. That would be great. Hopefully I can. That's a long ways from now, but who knows? Two more good rounds, you never know."