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The Yellow Jackets (1-0) rested many of their starters in the second half with Clemson visiting Bobby Dodd Stadium on Thursday.
Dwyer, the 2008 Atlantic Coast Conference player of the year, scored on the first play from scrimmage, taking an option pitch for a 74-yard touchdown.
He finished with 95 yards rushing on seven carries, including a 5-yard touchdown later in the first quarter.
Jacksonville State (0-1) trailed 31-7 at halftime, scoring on Brooks Robinson's 20-yard flea-flicker TD catch.
After Dwyer's first score, Jacksonville State fumbled away the ensuing kickoff when Anthony Barnes knocked the ball loose from Jamal Young, and Jemea Thomas recovered at the Gamecocks 23.
Scott Blair's 20-yard field goal ended that drive. The Yellow Jackets went up 17-0 on Dwyer's second TD run later in the first quarter.
Georgia Tech's Demaryius Thomas caught four passes for 101 yards. His 56-yard reception put the Yellow Jackets on the Jacksonville State 17 midway through the second quarter. Josh Nesbitt ended the four-play drive by running for a 10-yard touchdown on a quarterback keeper that made it 24-7.
The schedule gets no easier next week for Jacksonville State, as the FCS school visits Florida State.
Calvin Middleton led the Gamecocks with 59 yards rushing on 11 carries. Quarterback Marques Ivory completed 23 of 38 passes for 193 yards, two TDs and one interception that Georgia Tech safety Morgan Burnett picked off for the 11th of his career.
Nesbitt was 6-of-11 for 141 yards. Anthony Allen's 26-yard TD catch made it 37-10 early in the fourth quarter.
Georgia Tech's halftime lead was padded in the final minute when Jerrard Terrant returned a punt for a 58-yard score. It was the Yellow Jackets' first TD on a punt return in six years.
