The Pride tied the game with 48 seconds left in the fourth quarter to force overtime. Huntingdon took possession to start the extra period and Puckett's goal ended the game 23 seconds into overtime.
The win was Huntingdon's sixth straight over the Pride and the third overtime win in eight meetings with Greensboro.
Huntingdon (7-5, 3-0 USA South) played from behind for most of the first half on Sunday and trailed 5-2 late in the first half. Greensboro (4-5, 0-1 USA South) carried a two-goal lead into halftime before the Hawks took the lead.
Back-to-back goals by Seth Howe and Bryce Coates tied the game 5-5 in the first two minutes of the third quarter. Huntingdon took its first lead of the game with 8:16 left in the third quarter when Austen Saucier scored on an assist from Zach Barnhill.
Saucier scored two more goals on assists from Barnhill in a span of 93 seconds to give Huntingdon an 8-5 lead, its largest lead of the game.
Huntingdon would not trail for the remainder of the game, but the Hawks could not put the Pride away. Greensboro answered and tied the game 8-8 at the end of three quarters. In the fourth quarter, Huntingdon built a 10-8 lead, but the Pride answered and tied the game 10-10 with 3:18 to play.
Huntingdon took its final lead of regulation, 11-10, on a goal by Harper with 2:03 remaining in the fourth quarter before Greensboro tied the game to force overtime.
Saucier finished with five goals on five shots and Barnhill had two goals, four assists and four ground balls. Coates added two goals and Mac Puller had five assists. Harper finished with a goal and an assist, Howe and Puckett each had one goal and Tyler Keiser had one assist.
Keiser was 13-for-26 on faceoffs, picked up 10 ground balls and had two caused turnovers. Raymond Edwards finished with three ground balls.
Goalie Matt Murphy had 13 saves, 11 goals allowed and four ground balls.
Records: Huntingdon (7-5, 3-0 USA South); Greensboro (4-5, 0-1 USA South)
Coming Up: Huntingdon will play at Virginia Wesleyan on Wednesday at 6 p.m. (Central)