Levin finished early in the day, and when he completed play he was in front by six shots with a 36-hole total of 14-under 128 at the TPC-Scottsdale course. Harrison Frazar had closed that gap to three shots, however, when play was stopped by darkness.
Frazar had three holes to play when the action was suspended and had an outside shot to move into a share of the lead when the second round resumed Saturday.
A frost delay for the second straight morning pushed tee times back.
Levin has not won in his two years on the PGA Tour, but he finished among the Top 10 in his final two events of 2011 to wind up 31st on the money list.
He made six birdies through the first 16 holes Friday and attempted to hit the green with his tee shot on the 332-yard 17th hole. That shot bounced over the green into a bunker, but Levin holed his second shot from the sand for the eagle that highlighted his round.
Other than Frazar, no one was closer than six shots of the lead.
John Huh and Webb Simpson both were at 8-under 134 in a tie for third. Simpson shot a 69 despite a triple-bogey at the par-4 fifth.
Kyle Stanley, who let last week's event at Torrey Pines get away when he made a triple-bogey at the final hole, was alone in fifth at 135 following a 66. First-round leader Ryan Palmer was among those at 136 after struggling to a 72.
Phil Mickelson played the first nine holes Friday in 3-over, and then rebounded to shoot a 70 and easily made the cut at 138 in a tie for 28th place. J.B. Holmes, who returned to the tour this year after undergoing brain surgery in 2011, made his first cut of the season at 141.