The American world number five has gone bogey-free over the first 36 holes, the first player to do so since the event moved to the challenging Champion Course at PGA National in 2007.
"I'm definitely pleased about it," Fowler, 27, told Golf Channel after ending his round in style by sinking a 22-footer to birdie the par-four ninth.
"I felt like I didn't hit it as good as yesterday but I hit some really good drives through the middle, through the end of the round, and made a few more putts which was nice.
"So it was a good, solid day, a nice step in the right direction and I am really looking forward to the weekend."
Fellow American Jimmy Walker finished birdie-eagle to card 66 and trail by one shot, while Spaniard Sergio Garcia returned a 69 to trail by two.
World number three McIlroy, the 2012 Honda Classic champion, again struggled with his putting and iron play as he strung together a roller-coaster 72 that included a triple-bogey at the fifth, a double at the 15th, four birdies and a bogey.
That left the Northern Irishman at four-over 144, one stroke outside the cutline. Seventy-seven players advanced to the third round, including five-times major winner Phil Mickelson who made the cut right on the number after carding a 74.
"It's not easy," Fowler, who was beaten in a playoff for the Phoenix Open in his previous PGA Tour start, said of a layout where danger lurks at almost every corner with plenty of water and thick rough. "It takes a lot of out you, that's for sure.
"It's about getting yourself in the moment and committing to it and then trusting what you are trying to do...on a course where you've got to be spot on with the wind and the sections of the greens that you are trying to hit it in.
"There's a lot of trouble out there and it will jump up and bite you quick."
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Larry Fine/Andrew Both)
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