Knost had a chance to card a 62 and make history, but three-putted from long range on his final hole, the par-four 18th, for his only bogey as he finished at nine-under 135, a stroke behind early leaders Jonas Blixt of Sweden (67) and Germany's Alex Cejka (67).
Soon after, McIlroy was in good position to at least match Knost with a record-tying 63 as he teed off on his last hole, the par-five ninth, at nine under for the day but he wound up with a bogey to settle for a 64 and an eight-under total.
"I played well, I took advantage of the conditions," McIlroy told Golf Channel after benefiting from a calm morning of unbroken sunshine on a receptive layout in Ponte Vedra Beach.
"I don't feel like I played that much differently today than I did yesterday but it's an eight-shot difference. I'm in a good position even though I finished a little bit frustratingly, but these things happen."
With Day having made the most of a morning tee time on Thursday to seize a two-shot lead with his opening 63, McIlroy knew that he had to go low in the second round.
"This golf course plays so differently from morning to afternoon ... so you need to take advantage of it," said McIlroy.
"You can even feel as your round progresses in the morning, the greens are getting a little firmer, they are getting a little faster, the wind is getting up a little bit and it just plays trickier."
Knost, like McIlroy, had opened with a 72 and he soared up the leaderboard with a superb display of all-round golf highlighted by 10 birdies in his first 17 holes.
"I hit so many good iron shots today, and I made a lot of 10-footers," Knost said after finishing at nine under with fellow American Boo Weekley (69). "I really didn't make any long ones but I hit 18 greens so I had 18 looks at birdie.
"You do that around here you're going to shoot a good number because the greens are so small, you're not going to have very long putts. I let a few get away out there but it was a great day."
American world number five Rickie Fowler, the defending champion, was likely to miss the cut after following his opening 72 with a 71.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Andrew Both)
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