Dwyer's second touchdown erased a 34-33 deficit with 1:20 left.
He finished with 110 yards rushing on 24 carries.
Versatile quarterback Josh Nesbitt passed for 136 yards with one touchdown and rushed for 103 yards with one score.
Scott Blair booted four field goals, while Demaryius Thomas made two catches for 77 yards with one touchdown for the Yellow Jackets (11-2), who blew a 23-13 third-quarter lead, but won for the ninth time in their last 10 contests.
C.J. Spiller led Clemson with four touchdowns on 20 carries for a career-high 233 yards.
Kyle Parker went 10-for-17 for 91 yards with two interceptions for the Tigers (8-5), who have not won the ACC football title since 1991.