All three remain in the mix in a tie for 18th after signing for two-under 70s, three shots back of co-leaders William McGirt and Mackenzie Hughes (67).
McIlroy could now be forced to withdraw from the BMW PGA Championship which takes place in a fortnight's time and has a prize fund of £5.4million as the first event of the European Tour's Rolex Series.
Golf's top player Johnson is a stroke further back after recording an eagle, two birdies and three bogeys in a mixed bag for the U.S. Open champion, who has won three of eight events this season.
J.B. Holmes, Jon Rahm, Alex Noren and Chez Reavie share second.
Adam Scott had a one-shot lead when he finished with a pair of double bogeys. I felt a bit of stiffness on Sunday, hit a couple of drives that didn't feel quite right.
Australian Scott led at six-under heading to the famous island-green par-three 17th, but his tee shot found the water only a moment after U.S. Masters champion Sergio Garcia had made a hole-in-one. He has missed the cut twice and tied for 43rd twice in four starts, and has shot everything from 65 in the second round previous year to 81 in the second round in 2014.
Rory McIlroy had to birdie two of his last three holes to match Garcia's 73, the four-time major victor having double-bogeyed the 10th and 14th in his first tournament since getting married and signing a multi-million pound equipment deal with TaylorMade.
"I didn't have any other shot", he said.
Day's prospects of creating history looked bright when he played his first 11 holes in five under par, but the 29-year-old Australian bogeyed three of his last four holes and had to settle for an opening 70.
"I was going to play it Tuesday ... and I was just a little exhausted, so I just kind of took the day off", the 2007 champion told reporters.
"I knew I had to be kind of smart going at certain pins, trying to take opportunities when I had them and to not make any mistakes and obviously a clean card today was very good. Kind of nearly feel like you steal two when you birdie both the par-3s on the front", said McGirt.
McGirt was among 13 players from the morning draw who shot in the 60s, but he was the only player to get as low as 6 under until he missed a short par putt on the final hole.
He was 4 over through six holes to start this tournament and had not made up any ground until a birdie on the 16th, his ace on the 17th and a par save on the 18th for a 73. "And I overreacted probably a bit, but all in all, you just don't see that very often".
"I had a good birdie on 7 there, but 11 I had 250 front I think 279 hole, so I didn't think I could really hit 3-wood over the green".
Willett, who has been hampered by back problems throughout his career, struggled to an opening 79 on Thursday and had covered the back nine at Sawgrass in 40 before calling it a day.