Kody Adams led off the Panthers' first inning with a solo home run, his third of the year, for the team's other RBI.
Meanwhile, Stuckey (1-3) allowed just one earned run over seven innings to lead a pitching staff that did not yield a walk in the game. Jason Boulais and T.J. Sullivan each tossed one inning of relief and the trio combined for four strikeouts.
"It was a really well-played game on our part," Panthers head coach Greg Frady said. "It feels good to play like that as we had good at-bats and it was a high-confidence game. I really appreciate the effort of (the pitching staff) because when you don't walk anybody and play good defense then it's very tough for the other team to beat you."
Leading 1-0 after Adams' blast, GSU scored six runs in the third inning, highlighted by a two-run double from Wood.
Then with two outs in the eighth, Wood launched a no-doubt shot over the wall in left field with the bases loaded off Tigers reliever Shawn Gallagher to extend the lead to 15-2 as GSU would coast to victory.
The Panthers improved to 8-1 all-time against the Tigers and tagged starter Andrew Garren (1-5) with the loss.
Shields added two hits to extend a string of seven straight outings with at least two hits at the plate. Bennett also added two hits.
Wood's grand slam was his second long ball in as many games and 15th career home run. He finished with six RBIs in a game for the first time since 2010.
GSU will now play its first road series in Colonial Athletic Association this weekend, traveling to face George Mason for a three-game set, Friday through Sunday.