Glover birdied five of the first seven holes at the TPC-Louisiana course and completed 36 holes with a total of 12-under 132.
He has won three times on the PGA Tour, the second of those victories coming at the 2009 U.S. Open. His only victory since then came two years ago at the Wells Fargo Championship, an event that will be played next week in North Carolina.
Boo Weekley was alone in second at 133 following a 68 and D.A. Points was by himself in third at 134.
Morgan Hoffman posted a 135 total for fourth place and Ernie Els, who was the runner-up in New Orleans a year ago, was fifth at 136.
Guan Tianlang, who at age 14 finished as the low amateur at the Masters two weeks ago, survived the cut by producing a 3-under 141 total. First-round leader Ricky Barnes, who had made the cut in just three of his previous 10 tournaments this year, faded with a 76 and wound up at 140 for two rounds.