Vijay Singh, who holds the tour record for most victories over the age of 40, was a shot back.
Villegas shot his second straight 68 and Kim equaled the course record with a 64, leaving them tied at 8-under 132. Singh, who won this tournament 11 years ago, was alone in third place at 133 following a 66 at the PGA National course.
Both Villegas and Kim won twice in 2008, but neither posted a victory last year.
"I'm not going to say last year was a bad year," Villegas said. "I played 27 events and I missed two or three cuts. So it was a very consistent year. I've made the cut in every major. But it was a little frustrating because I felt I should have played a little better than I did."
Kim's round was highlighted by a chip-in for birdie at the par-3 seventh.
"I've been working hard on my game and the last couple of months I've really started to play better," Kim said. "I haven't put four good rounds together."
Jerry Kelly was alone in fourth at 134 while former Masters champion Mike Weir was part of a group at 135.
Swim Week Miami Beach 2014 [PHOTOS]