Wagner and Tommy Gainey were tied for the top spot at the Old White TPC Course at the Greenbrier Resort. They had a two-shot advantage over 2012 U.S. Open champion Webb Simpson and Jin Park.
Both Wagner and Gainey won for the first time in their PGA Tour careers last season, but neither has posted a victory this year.
Simpson had a legitimate chance at firing a 59, reaching 8-under par with six holes to play. Birdies on three of the final holes remaining would have allowed him to break 60, but he wound up with pars on all six.
He played a 10-hole stretch in 8-under beginning with the par-3 third. Wagner's round was highlighted by an eagle at the par-5 12th.
"When I made that eagle I definitely was thinking 59 the rest of the way," Wagner said. "I hit a lot of good shots coming in. I hit a lot of good putts. I think I wanted it a little too bad and they just didn't drop, but it's nice to be disappointed with 62 as opposed to being disappointed with 76s as I have been lately."
Tag Ridings, Steven Bowditch, Daniel Summerhays and Neal Lancaster shared fifth place at 65.
Jordan Spieth, who at age 19 held the 36-hole lead last week at the AT&T National, fired a 67 in the first round. Phil Mickelson struggled to a 74 in a round that included a triple-bogey eight at the 17th hole.