"I hit drivers on holes today where I would never have the last few years", McIlroy said.
While Rose dropped three shots in one hole, American Harris English picked up the same number with an albatross at the par-five 11th, where his second shot from 235 yards landed softly a couple of paces in front of the cup and rolled in.
SportsLine's prediction model, built by DFS pro Mike McClure, has nailed four of the past eight majors entering the weekend and called Tiger Woods' deep run in the PGA Championship despite being a 25-1 long shot.
"You've got all these funky lines and in May it gets firm". However, I think I've nearly secured my card for next season, so it releases some stress a little bit and this will allow me to play my own game.
Meanwhile, Fleetwood passed the "ultimate test in golf" with flying colours on the opening day.
The pair signed for a creditable two-under-par 70, while in-form Englishman Tommy Fleetwood and Keegan Bradley shared the lead at seven under with 65s.
Jim Furyk described the par-three 17th as the place where golfing ghouls come "to watch the vehicle wreck" and there was plenty of carnage during the opening round to satisfy the massive gallery at the Island Green as 14 balls hit the drink.
"I played really well all day apart from I hit a poor tee shot on 14 and got away with it", Fleetwood said. "I had some chances on 15 and it didn't happen but it shows that if you stay patient, things can happen". It's one of the courses that's the ultimate test in golf.
McIlroy, a presence on leaderboards every time he has played this year, got off to a good start with a bogey-free sortie.
"I've played well here in the past and if I drive it well that's a massive key for me".
Fleetwood finished seventh at Sawgrass a year ago and third in the Arnold Palmer Invitational on Sunday, when Francesco Molinari stormed through the field to win his second PGA Tour title.
"I'm comfortable with my game, doing everything well", said the Northern Irishman, who for all his good play this year is yet to win. And with a win this week, Woods would tie Jack Nicklaus for the most victories in the history of the Players Championship at three.