Cooks made 8 of 11 field goals and Davenport hit 5 of 7 while the rest of the team shot just 38 percent (17 of 45). Jimmy Gavin scored 13 and Keon Johnson had 12 points for Winthrop (3-0) which opened the season with three straight wins for the first time since the 2009-10 season.
The Eagles took a 41-31 lead into halftime and a jumper by Roderick Perkins gave them a 17-point cushion with 11 minutes to play.
Jacksonville State (2-3) answered with a 9-0 run to make it 61-53 fewer than two minutes later and trimmed its deficit to 6, 72-66, on a jumper by Malcolm Drumwright with 2:44 left, but Winthrop scored 8-straight to seal it.
Erik Durham led Jacksonville State with 15 points.