The Monarchs (16-6, 6-0 USA South) won game one 8-1 and then took a 5-4 eight-inning victory in the nightcap.
Shenandoah (13-5, 4-2) had runners on the corners with no outs in the eighth inning of game two, but could not push the tying run across.
Down to its last out in the seventh, the Hornets tied the game at 4-4 on an RBI infield single from sophomore Brittany Guepe.
Guepe drove home pinch runner Maggie Waters, who had been moved to second on a sacrifice and third on a fielder's choice.
Methodist drew first blood with three runs in the second before Shenandoah tied it with a three-run third.
The Monarchs scored the winning run as placed runner Katie Byrd was sacrificed to second and came home on an Erica Bradley single.
Coble, McCabe and Denise Mitchell all had two hits in the game for the Hornets.
Jessica Farmer (7-4) held SU to just five hits in the opening game as MU broke open a 1-1 contest with three runs in the fourth and four in the seventh.
Mitchell had two of Shenandoah's five hits.
Senior Brooke Over (6-4) took the loss in both games. She struck out three in the opening game as the starter and another three in 4 2/3 innings of relief work in game two.
SU hosts No. 11 Christopher Newport on Tuesday at 3:30.