Bailey (3-5) struck out seven, walked one and induced 12 straight outs after hitting the first two batters of the game.
The 20-year-old right-hander gave up a single to Jai Miller with two outs in the fifth inning, but recovered to retire the next seven batters in his longest outing of the season. He had taken no-hitters through the sixth twice this year.
Reliever Jan Granado pitched a perfect eighth and earned his first save, despite yielding two runs on two hits in the ninth.
The Reds (24-32) manufactured runs in the second and seventh to put Bailey on the path to his second win in his last four starts.
Sarasota recorded three key runs, all unearned, in the eighth. The outburst was highlighted by Drew Anderson's RBI triple, but Sarasota also scored on wild pitches by relievers Jesus Delgado and John Mangieri.
Juan Figueroa's two-run shot with two out in the ninth finally put the Hammerheads (24-31) on the board.
Starter Jacob Marceaux (0-5) took the loss after giving up one run on three hits over four innings. He struck out three and walked two as the teams split the four-game series.
Marissa Rega is a contributor to MLB.com. This story was not subject to the approval of the National Association of Professional Baseball Leagues or its clubs.