On a hectic day at the Muirfield Village Golf Club, Phil Mickelson shot a 79 and withdrew, Rory McIlroy battled back from a quadruple bogey to finish under par and Tiger Woods quietly put together a 70 that put him in contention.
Stallings emerged as the leader at the Jack Nicklaus-hosted tournament with a 6-under 66, one shot better than Spencer Levin and two-time heart transplant recipient Erik Compton.
Until late in the day, no one who had finished the round or was on the course was better than 3-under par and there were as many as 30 players within three shots of the lead.
Stallings, however, birdied three of the last four holes to produce a sub-par round for the first time since the Masters.
Woods turned in his 70 despite making a double bogey at the 18th and shared 11th place with a large group that included Ernie Els and recent tour winner Ben Curtis.
McIlroy shot a 71, but he had to come back after making a seven at the par-3 12th hole, his third of the day. After putting his tee shot in a greenside bunker, McIlroy blasted his ball all the way across the green into the water. After taking a penalty drop he put his fourth shot into another bunker, blasted out and two-putted for the quadruple bogey.
McIlroy, the world's second-ranked player behind Luke Donald, has missed the cut in his last two starts.
Bubba Watson, playing for just the second time since his Masters victory, bogeyed four of the last eight holes and shot a 75. Defending champion Steve Stricker played the final six holes in 4-over and had a 73.
Mickelson cited exhaustion when he withdrew from the event. He said he was not ill or injured.