Hickbottom, who was 12 of 24 for 208 yards, connected with Darrell Clark for 35 yards and Devante Davis for 15 to help the Tigers (5-4, 4-2 Southwestern Athletic Conference) take a 17-13 lead at the half.
His 47-yard hookup with Kobe Ross on the opening drive of the third quarter proved to be the difference.
Johntavious Robinson ran for 130 yards for Grambling and Hickbottom added 99. Davis had 91 yards on three catches.
Chris Fowler's 22-yard connection with Booker Chambers midway through the third quarter pulled the Delta Devils (1-7, 1-4) within 24-19 but Grambling's defense took over.
Dejerric Bryant gave MVSU a 7-0 lead with a 7-yard touchdown run on the opening possession of the game and John Derrick Smith scored on a 5-yard run with 1:19 left in the first half. Tracy Thompkins had 15 tackles for the Delta Devils.
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