Fellow freshman Casey Turgeon then drove a fastball over the right field fence to give the Gators a 2-1 lead.
"I just got a pitch I could handle and put a good swing on it," Turgeon said. "I had two strikes on me, so I was ready for anything he threw."
The Eagles fought back. Catcher Andrew Valencia, who went 4-12 on the series, lined a two-out double into the right-center gap to score Alex Diaz and tie the score at two in the sixth inning.
That's when Gushue did his damage.
The freshman drove a 1-2 pitch onto the road behind right field to give Florida a 3-2 lead it would keep. Forjet left a slider hanging in the middle of the plate with two strikes, and Gushue came up with another clutch hit for the Gators.
"I just wanted to put it in play, and it ended up going out," Taylor Gushue said with a laugh. "(Forjet) was mixing it up a lot. I only saw one fastball today."
The 2-5 hitters in the Florida lineup combined to go 0-13.
The Gators got a strong performance out of sophomore right-hander Jonathon Crawford. He went 5.2 innings, allowing five hits, two runs, one walk and striking out three hitters. His command has improved during each outing this season.
"Our pitching was outstanding," Florida head coach Kevin O'Sullivan said. "It was great to get Crawford out there. Each time he goes out there, he seems like he's getting better and better."
Daniel Gibson (1-0) relieved Crawford after the two-out double by Valencia. Three of the seven outs he recorded came on the ground. The other four were strikeouts. The only batter that reached against Gibson came on a throwing error by Turgeon.
"That's probably the best he has thrown since he has been a Gator," O'Sullivan said.
Florida hosts No. 12 Florida State on Tuesday at 7 p.m. O'Sullivan said after the game he hasn't decided on a starting pitcher. The Seminoles are expected to start freshman right-hander Luke Weaver (0-0, 20.77).