The Jamaican currently holds world records in the 100m, 200m and 4x100m with times of 9.58s, 19.19s and 36.84s respectively
Kuchar was atop the leaderboard for a third straight day after a one-under par 70 at Riviera Country Club.
Playing partner McIlroy carded a three-under 68 while Australia's Scott grabbed his share of the lead with a birdie at 18 to cap a four-under 67.
They were all tied on 10-under par 203 - one shot ahead of Russell Henley and Harold Varner on a jam-packed leaderboard.
Tiger Woods, who came into the week gunning for a record-setting 83rd US PGA Tour title, was nowhere near the top, however, after a five-over par 76 that left him languishing 15 off the pace.
Kuchar started the day with a two-shot lead and maintained his cushion with three birdies through 11 holes.
But three bogeys in four holes from the 13th through the 16th opened the door for McIlroy, who tied the lead with his fourth birdie of the day at 13 and despite a bogey at 14 was one shot ahead until Kuchar got up and down for birdie from a greenside bunker on the 17th.
Scott, first in the clubhouse on 10-under, was looking forward to challenging for a victory on the same Riviera course where he hoisted a trophy in 2005 but couldn't claim an official win because the rain-sodden event was shortened to 36 holes.
He also has two runner-up finishes.
"I think all of that is just a bit of motivation for me to win here and have an official victory at Riviera," Scott said. "I think that would be extremely satisfying for me."
The Aussie veteran is coming off an eight-week break, but said at this stage of his career he's not too worried about rust.
"I almost feel like I know what I'm doing after 20 years of having a season and having a break and coming back out," Scott said. "I know what this course demands of you."
Riviera's challenge is slightly different this year thanks to the warm, dry weather in what is usually Southern California's rainy season.
"I think it's fun to see it this way in firm, fast conditions," Kuchar said. "Any time you get greens firm it is hard to get them close to the hole, a golf course just plays that much harder."
McIlroy opened with a birdie at the par-five first, but didn't pick up another shot until back-to-back birdies at the eighth and ninth.
"I hit it well all day, but I felt like every time I hit a decent shot I left myself on the wrong side of the hole," he said. "And the putts that I had were very defensive, downhill, big breakers, trying to play enough break, trying to die them in.
"Especially on this golf course, they're very tricky, very difficult to make," McIlroy said. "So I just kept telling myself to stay patient."
Putting was Woods' undoing in a round that included a four-putt from 18 feet at the 13th and a three-putt bogey to close his round at the ninth.
Woods also had a four-putt at Torrey Pines last month, making it his first season since 1998 with multiple four-putts.
"I didn't putt well today at all," said Woods, whose well-documented struggles on Riviera's greens are a key reason he has never won here in 13 prior starts.
"I didn't have a feel for it, I didn't see my lines. I couldn't feel my pace an I was just off."
Plenty of players are within striking distance of the leaders.
Dustin Johnson, whose 2017 Riviera victory propelled him to number one in the world, had six birdies and an eagle in a four-under 67 and was tied on 205 with Joel Dahmen.
It was a further stroke back to Max Homa, Talor Gooch and Kang Sung, with Jon Rahm and Hideki Matsuyama among a group of six players just four back on 207.
The Jamaican currently holds world records in the 100m, 200m and 4x100m with times of 9.58s, 19.19s and 36.84s respectively
Total property income posted year-on-year growth of 10% to $74m, highest value ever
All official donation channels however remain open through the outlets announced by government agencies
The Starlight Park is a four-building freehold community in Meydan
The 22-time major champion admits his farewell tour hasn't been as enjoyable as he would have hoped
Eating out, poor hand hygiene and erratic weather may be among causes, say medics
The goal-scoring striker is suffering from a muscle injury sustained during the Champions League quarter-final loss to Real Madrid
Lieutenant General Abdullah Khalifa Al Marri, Commander-in-Chief of Dubai Police, made the announcement on Wednesday