Kirstyn Arcata finally snapped the scoreless draught with a free throw at the 3:55 mark, but Shenandoah was unable climb all the way back.
Arcata's free throw started a 10-1 spurt for the Hornets, which put SU down just two, 64-62, with 87 seconds left, only to see the Wasps answer with a 3-pointer on the ensuing trip down the floor and close out the victory.
E&H made was 7-of-11 from the line in the final 41 seconds to clinch the win.
Taylor Blevins had 15 with Sydney McKinney chipping in 13 points and 12 rebounds for the Wasps.
Emory & Henry had a 41-32 advantage on the glass but Shenandoah scored 14 of the game's 22 second chance points.
Both teams were 23-of-55 from the field (42 percent) with E&H making nine 3-pointers to the Hornets six.
The Wasps had a 17-16 lead after one and led 35-31 at the break.
Shenandoah continues ODAC play on Monday with a 7 p.m. home game versus Randolph.