Van Pelt, who shared the lead after the opening 18 holes, shot a 6-under 66 over the Warwick Hills Golf & Country Club course.
He opened his round by chipping in for birdie and went on to post a two-day total of 14-under 130.
Dudley Hart (68), another of the first-round co-leaders, was at 132 along with Daniel Chopra (67). Woody Austin (67) and Matt Jones (63) were tied for fourth at 133, and Fredrik Jacobson (66) and Bubba Watson (67) were another shot back.
"I knew the scores were going to be low again, and if I wanted to stay near the top I needed to keep going forward," Van Pelt said. "That's just kind of what I kept telling myself all day. Even after I got off to a good start, I was just trying to stay aggressive and make birdies."
Van Pelt is looking for his first PGA Tour win.
Corey Pavin, who was tied with Van Pelt and Hart after the first round, shot a 74 and fell into a tie for 29th at 138.
Swim Week Miami Beach 2014 [PHOTOS]