Shenandoah (4-3, 3-1 USA South) is over the .500 mark at the latest point in the season since winning the league title with a 7-3 regular season record in 2004.
The Hornets led 40-7 before Methodist (1-6, 0-4) converted a pair of Daniel Wright interceptions into second half scores.
SU then put the game way with a Wright to Stephen Dellinger TD pass with 9:31 to play; MU blocked the ensuing PAT for a two-point conversion which also closed the book on the day's scoring.
Shenandoah rolled up 266 yards of total offense in the first half on its way to a 33-7 lead.
It took little time for the Hornets to take the lead – SU forced a fumble on the opening kick and two plays later Brad Martz rumbled in from the 3 for the initial touchdown of the contest.
Martz was in position for the three-yard TD run thanks to a 26-yard Wright to Rico Wallace completion on Shenandoah's first offensive play.
Wright's second touchdown pass of the half, 19-yards to Qiydaar Murphy 18 seconds before halftime, gave SU that 33-7 advantage.
Shenandoah had 223 yards of offense in the second half, but allowed Methodist to hang around thanks to three interceptions.
Wright finished 18 for 29 for 220 yards and the three TDs.
Wallace had seven catches for 128 yards; all but one of these receptions and five of the yards came in the first half.
Joseph paced a rushing attack with 149 yards and two TDs on 28 carries.
Byron Mitchell had seven tackles (six solo) on the defensive side of the ball.
Shenandoah plays its final home game of the regular season next Saturday night against Ferrum. Game time is 7 p.m.