Poyner allowed two walks while Young, Harris and Magliozzi threw perfect innings, combined for three strikeouts in the final three innings of the game.
But it was Poyner (3-2) that set the tone.
The sophomore left-hander didn't allow a base runner in four of the six innings he pitched, throwing just 85 pitches and recording two strikeouts.
"Outstanding. You give up one run over six, you pitched really good," Florida head coach Kevin O'Sullivan said of Poyner. "He threw strikes, kept the ball down and we played really good defense behind him. We don't want deep counts. We want to throw it over the plate and make quality pitches. We played really good defense behind him."
The impressive part of Poyner's outing is that he made it after throwing 56 pitches in his start on Friday at LSU, allowing three runs in 4.1 innings. He said there was some extra running and time spent in the training room to get his body ready for such a short turnaround, but Poyner said his arm felt ready to go.
"I felt pretty good," Poyner said after tossing a career-high six innings. "I was just throwing it over the plate and let the defense play. We made really good catches in the outfield and played really good defense in the infield."
Six of Florida's seven runs came in the fifth inning. During the second time through the order. the bottom half of the lineup started to get better swings on Florida Atlantic starting pitcher Jake Meiers.
After Meiers hit Josh Tobias with a pitch to start the inning, he got a ground ball to shortstop Mitch Morales, who tried to start the double play but threw the ball into right field, giving the Gators first and third with no outs instead of erasing the runners with a double play.
The damage came soon after. Cody Dent started it by tying the game with a squeeze bunt, and Casey Turgeon broke it open two batters later with a two-run double. After a run-scoring balk, a Zack Powers RBI single and a walk to Harrison Bader with the bases loaded, the Gators had some breathing room with a 6-1 lead after the fifth inning.
"We started figuring out the pitcher a little bit and started putting good swings together," Turgeon said. "That's how big innings happen."
The win also served as the 250th win at Florida for O'Sullivan.
Florida is now 27-23 with six regular season games left. The Gators have to remain about .500 at the end of the SEC Tournament to be eligible for the NCAA Tournament.
The Gators will practice on Wednesday and Thursday before hosting Auburn for the final home series this weekend, starting Friday at 7 p.m.