"They made a lot of big plays. We made a lot of big plays," first-year Corinth coach Doug Jones said. "The biggest thing that won the game for us was defense."
Corinth improved to 4-0. The Bulldogs (2-3) lost their second straight.
New Albany had pulled within 21-13 on quarterback Spencer Day's 1-yard sneak with 3:59 to play, but Hill kept the lead at eight.
"When they lined up, they brought a new guy in," Hill said. "I said, 'This is my opportunity. I know we need a play.'"
New Albany got it back on its own 42 with 23.5 seconds left and scored in dramatic fashion, a hitch-and-pitch as time expired.
Day lined a pass to Chandler Nail, who drew a pair of defenders and pitched to Boston Newsome who won a race 30 yards to the end zone. Newsome, though, was stopped on a two-point run attempt.
"That's just a play we've had in now for about three years," New Albany coach Ron Price said. "Chandler made a great catch and pitch."
New Albany finished with 133 yards rushing and had 22 at the half. It had 66 passing. Corinth finished with 103 on the ground and 85 passing in a defensive struggle.
The Bulldogs punted on each of its first five possessions, and Corinth got good field position in return.
Robert White rushed 5 yards for the Warriors' first touchdown on a 35-yard drive. Corinth quarterback Brady Allen hit Brice Spence between tacklers for a 77-yard touchdown and a 14-0 lead in the second quarter.
New Albany pulled within a score on a 15-yard run from Kachius Clay on a drive that started at the Corinth 20 thanks to a 19-yard punt. Gwyn put Corinth ahead 21-7.
Day's 1-yard sneak was set up by a fourth-and-28 pass to Nail for 32 yards to the 1.
Robert White had 64 yards on 21 carries for Corinth. Newsome had 80 on 18 touches for the Bulldogs.
Click here for a photo gallery of this game.