Barrett (9-1) worked six innings, allowing five hits and two walks while striking out six.
Strzelecki walked one and struck out one while pitching the seventh and eighth innings.
Gamble got three straight strikeouts in the top of the ninth.
"Jordan's been phenomenal for us all year," said Head Coach Al Corbeil. "I didn't think he had his best stuff today, but he battled, competed, threw some big pitches. We did enough to win. I'll take a shutout any day of the week.
"Joe threw really well again, and Gamble did what he's done for us almost every time out all year. He was sharp. His stuff was real good tonight. He and Barrett have been huge for us all year. "
The Panthers had chances to score in the first and second innings, but stranded a runner at third base in each frame.
Kaylor Kulina went one-for-three to extend his hitting streak to 23 consecutive games.
In addition to his RBI single, Piatt walked and stole a base.
The Eagles (31-13, 13-6, No. 4 FCSAA) face South Florida again tomorrow at 1 p.m. in Avon Park.