The kick capped a 35-yard drive over the final 33 seconds after UTC scored the tying touchdown and two-point conversion.
Sophomore receiver Gabe Chambers set the winning drive in motion with a big kickoff return to midfield.
Quarterback Marques Ivory completed three straight passes, including a sideline pass to former high school teammate Kevyn Cooper to get it going. Damarcus James, carrying the biggest load in the running game following the suspension of senior Washaun Ealey, then broke off a 13-yard run to set up the field goal.
The Gamecocks were able to call time out just before the clock expired.
Griffin also hit a 33-yard field goal to open the scoring.
UTC (0-2) tied the game on a 16-yard Jacob Huesman pass to Ron Moore with 39 seconds left. Keon Wiliiams scored the two-point conversion to tie the game.
The Gamecocks (1-1) led 17-0 late in the first half. UTC scored its first touchdown of the game with one second left in the second quarter.
James led the Gamecocks with 120 yards rushing on 16 carries. Freshman Troymaine Pope from Anniston had 100 yards on 12 carries. It was the first time JSU had two players rush for 100 yards since 2008 vs. UTC. Ivory completed 14 of 19 passes for 156 yards.
UTC freshman quarterback Jacob Huesman rushed for 166 yards and completed 18 of 30 passes for 181 yards and two touchdowns.
The Gamecocks are off until Sept. 22 when they play Eastern Kentucky in their conference opener.