Presley and Ryan Blumenthal combined to make four straight free throws in the final 18 seconds to cement the lead.
The win gave the Hoyas, and coach Robert Churchwell, a 7-3 record and an early Christmas present to build on.
"That was nice to see," Churchwell said of the free throws. "It's a big difference, considering Monday, we missed 20 free throws."
With the victory, Harrison will take some momentum and confidence with it when it heads to Miami after Christmas to play in the Adidas Slam.
It didn't look good for the Hoyas early as Sprayberry jumped to a 13-point lead in the first half. But Harrison closed the second quarter on a 16-4 run, capped by Presley's 3 at the buzzer, which gave the Hoyas a 33-31 lead at the break.
"That was real big," Churchwell said, "to go up at the half after trailing by 13. It was nice to go into the half with the lead."
After Sprayberry tied the game at 37-all 2 minutes into the third quarter, Harrison gradually began to build a lead. Three-pointers by Presley and Ryan Blumenthal, who had a game-high 16 points, pushed the advantage to 57-50 with 5:20 to play.
But Sprayberry's Duncan Lunsford, who finished with 15 points, scored on a layup and added three free throws to cut the lead to 59-55. Alijah Bennett's 3-pointer from the corner made it a one-point game and Lunsford followed with a driving layup to give the Yellow Jackets their first lead of the second half, 60-59, with 50 seconds to play.
"We wanted to apply pressure for four quarters," Sprayberry coach Marc Carver said. "We wanted to have a chance to win the ballgame at the end, and we did. The difference was Harrison made their free throws and we didn't."
Harrison went 14-for-17 from the line in the second half, while Sprayberry was 12-for-20.
While the loss dropped the Yellow Jackets to 5-4, Carver said his team's experience in the tournament, where it beat South Cobb and Woodward Academy to reach the finals, would pay dividends.
"The tournament should have given us some confidence going forward," he said.
Guilmette finished the night with 15 points, while Presley had 12 for Harrison.
Trey Schultz added 15 points for Sprayberry.