Rose, 37, sneaked past the cut but sunk seven birdies on Saturday to go within two shots of the leaders at four under.
But not necessarily at the British Open. He is even par overall.
Round of the day was England's Tommy Fleetwood as his six-under score of 65 moved him to within one of the lead. He missed an 8-footer on No. 5 for the outright lead.
After making birdies at the fourth and the sixth, Woods drilled a 40-foot bomb at the ninth.
Drives of some 400 yards were commonplace and with only wispy rough and little wind, low scores were plentiful in the benign conditions.
Woods began the day six shots back.
Kevin Kisner plays a shot out of the bunker at the British Open at Carnoustie, Scotland on 19 July 2018. The 14-time major champion's birdie putt from 8 feet at the 18th rolled just past the right edge.
He still made bogey.
McIlroy, who is seeking a first major title since 2014, was part of a large group on two under par which also included Spain's Jon Rahm, world number two Justin Thomas, 2015 victor Zach Johnson and the English pair of Danny Willett and Matthew Southgate.
Compared to how he finished his first round Spieth was more than happy to negotiate the daunting closing holes with no further damage and his name lurking on the leaderboard. He is even par for the tournament.
McIlroy was particularly perturbed by his meek display in the final round of the Masters in April, which he started three shots off the lead and was only one back after two holes.
Nor should he. Zach Johnson, victor of a Masters and that British Open, has put himself in fantastic position to have his name engraved on the cherished Claret Jug for a second time. Perez was tied for the lead until he hit into a bunker on the 18th hole and took bogey. Tiger Woods teed off early Friday morning after playing the afternoon on Thursday.
And speaking of those 20-somethings, Kisner's wet-and-wild double gave new life to Rickie Fowler, who is only 3 strokes back, and to defending Open champ Jordan Spieth, also only 3 back. A rugged start, a strong recovery, a few putts for birdie, a few he missed for par, and it added to an even-par 71.
It wasn't easy on everyone.
But at least he's still playing.
Justin Thomas (77), the world No.2, failed to make the weekend on 146.
It looked like he would miss the cut at Carnoustie, only to birdie the 18th on Friday to move to three over and ensure he would return at the weekend. He was nine shots behind Zach Johnson and Kevin Kisner, who shared the lead at Carnoustie on 6-under 136.
"One-over on the last four certainly beat yesterday", Spieth, who endeared himself to the galleries by throwing the odd ball to young fans calling his name, said.