Rose and Gillis set Honda pace
England's Justin Rose went to the turn in 31 and shared the lead midway through his second round at the Honda Classic in Florida on Friday.
With three PGA Tour titles to his name in the last two seasons, the 31-year-old was eight under par and alongside self-confessed "journeyman" Tom Gillis on a day when another American, left-hander Brian Harman, shattered the course record by three with a dazzling 61.
Rory McIlroy, who will be crowned golf's new world number one if he wins on Sunday, was only three behind with eight holes remaining, but Tiger Woods (68) and Lee Westwood (69) were seven adrift.
Rose, who matched McIlroy's 66 on the opening day, got back on the birdie trail with a nine-foot putt at the 12th - his third - and then converted chances from 18, 15 and 14 feet on the 15th, 16th and 18th.
Former European Tour player Gillis, now 43, matched the old course record with his 64, but that was totally overshadowed when Harmon - first reserve for the event at the start of the week - turned in 29 and stood on the tee at the par five 18th needing an eagle for 59.
He was in a greenside bunker for two, but splashed out five feet past the cup and missed it.
"Just to have a chance to do something special like that is really humbling and pretty cool," he said. "I just got it rolling today - it was one of those days where everything bounced my way and I made a lot of putts."
Woods was in danger of missing the cut when he pulled his tee shot into the water on the short fifth - his 14th - and double-bogeyed.
With two to play he was in 71st place and only the top 70 and ties at the end of the second round progress to the closing 36 holes, but he then closed with back-to-back birdies.
On the eighth Woods hit a 138-yard approach to six feet and he followed that putt with an 11-footer on the next.
"It was a little bit of a fight - probably the worst I've hit the ball in months," he said. "I got it going, lost it, got it going, lost it and then got it going.
"I figured something out with the swing the last four holes. Unfortunately it took me that long.
"It was a grind, but I scored. That's something I can take out of the round - and I know I putted a lot better.
Graeme McDowell was another to shoot 64 and moved from three over to three under. Padraig Harrington was one further back after a 68, but Open champion Darren Clarke missed the cut on eight over after adding only a 75 to his opening 73.
Westwood had only one bogey on his card - it came at the short 17th for the second day running - but managed just two birdies. He and Woods were just outside the top 30.
Overnight leader Davis Love, America's Ryder Cup captain, was seven under and third on his own after a back-nine 34.
Rose went two clear by adding more birdies from five feet at the long third - he almost sank his bunker shot - and 13 feet on the fifth.
McIlroy could not get up and down from a plugged lie in sand at the 13th, but on the next hit a superb 179-yard second to two feet and returned to five under, five behind.