The Hornets (7-6, 2-2 ODAC) made 15 of their first 20 shots from the field (75 percent) to take a lead they would not relinquish over H-SC (4-9, 1-3).
The two teams were tied on five occasions in the initial 13 minutes of play before SU closed the half on a 14-6 run to take a 44-36 lead at the break.
Shenandoah was on fire in that first 20 minutes, making 18-of-29 of its shots (62 percent) from the field and seven of an eventual program-record 14 3-pointers.
Senior Kwa McDonald, classmate Aaron Patterson and sophomore Christian Meredith, the three Hornets who finished with double-digit points, were a combined 7-of-11 from long distance in the opening stanza.
Meredith, who was 5-for-6 behind the arc on the day, had 17 points to 18 for Patterson and 10 for McDonald.
"I thought our offense was phenomenal in the first half," Hornets coach Adam Walsh said.
"We have been talking about putting two halves of basketball together, and I thought we did that today.
"When guys see shots fall on the offensive end, it is much easier to play defense.
"I was very proud of the defensive effort in the second half."
Leading by eight points at the break, Shenandoah saw the Tigers cut the deficit to three, 53-50, following a Chaise Johnson jumper with 13:03 remaining.
SU answered that bucket with a 13-0 run, holding H-SC off the board for 4:12 to effectively seal the victory.
The Hornets lead was in double digits for all but 45 seconds of the final 10:53 of the contest.
After Malik Crute brought the visitors to within nine, 67-58, on a layup at 4:51, Shenandoah ended the game on an 18-7 run to claim the 20-point win.
"That is a great result (to have the largest margin of victory)," Walsh said. "With what we have been building and our collective effort, those are the types of results that will happen."
SU shot 55 percent (31-of-56) for the game and had a 38-30 edge on the glass.
Crute had 16 points for H-SC.