Jackson hit the first pitch he saw inside the bag at first base for a leadoff triple in the bottom of the first, and Gardner-Webb (11-7) scored three runs in that inning to go in front for good.
The Runnin' Bulldogs added two runs in the second, two runs in the fourth and two more in the fifth to go up 9-0 - before Alabama State (6-14) answered with a pair of singles in the top of the sixth to break up the shutout.
Gardner-Webb added three more runs in the sixth, getting an RBI double from Ryan Hodge and an RBI hit from Danny Yelverton to push the lead to 12-1. After Alabama State added a pair of runs to cut the lead to 12-3, the Runnin' Bulldogs added its final run in the bottom of the eighth on a bases-loaded wild pitch that plated Adam Tiller.
The Hornets plated three runs in the top of the ninth for the final margin.
Brock Wilson (3-2) picked up the win, working 7.0 innings, striking out six and scattering seven hits. The big righty retired 10 Hornets in a row during a stretch that spanned the second through the sixth inning.
Jackson (4-for-4, 2B, 2 3B, 3 runs, 2 RBI) had a strong day at the plate to lead Gardner-Webb's 14-hit attack. Ryan Hodge (3-for-5, 2B, RBI), Scott Johnson (2-for-4, 2B, 3 RBI), John Harris (2-for-4, 2B, RBI) and Danny Yelverton (2-for-4, RBI) each had big days at the dish for the Runnin' Bulldogs, who tied a season-high hit total as a team.
Alabama State starter Joel Alvira (1-2) took the loss, allowing seven runs (four earned) on eight hits in four innings.
The Hornets collected eight hits Friday, with Richard Gonzalez going 2-for-4 with a pair of runs scored and an RBI to pace that effort. Derrick Sanders (1-for-2, RBI) and Emmanuel Marrero (1-for-3, RBI) also drove in runs.
Gardner-Webb and Alabama State will play a doubleheader Saturday afternoon at 1:00 at John Henry Moss Stadium/Bill Masters Field.