Villegas eagled the par-5 18th hole to shoot a 6-under 64 on a day of unusually low scoring at the PGA National course.
There were 60 sub-par scores recorded on a course that normally produces some of the most difficult conditions on the PGA Tour. A score of 4-under par has won the event twice in the last decade.
Villegas won this tournament three years ago and has not had a victory since. He missed the cut nine times in 25 tourneys last year and also missed the cut in two of his three previous starts in 2013. Villegas failed to finish among the leading 125 money winners last season and is no longer is fully exempt to play on the tour.
He had a one-shot lead over Branden Grace, Robert Streb, Graham DeLaet and Rickie Fowler, who revealed Thursday he has been playing with a sore back since last summer.
Boo Weekley, Sean O'Hair, Fabian Gomez, Lee Westwood, Billy Horschel, Ben Kohles, Seung-Yul Noh, Brian Stuard, Doug LaBelle and Tournament of Champions winner Dustin Johnson were all at 66 -- two shots behind.
This was only the fourth competitive round of the year for McIlroy, who missed the cut in an early-season European tournament and then was eliminated last week in first round of the World Match Play Championship. Woods has also suffered a missed cut and a first-round match play elimination in 2013, but in between he won the tour stop at Torrey Pines in California.
Villegas admitted his recent poor play had left him downcast.
"This game is great when you're playing good," he said. "But when you're out here missing cut after cut, it's not that much fun."