The Quakers (11-2, 4-0 ODAC) led virtually throughout in taking out the Hornets (5-8, 1-3).
Gabriel Gonzalez stopped the scoreless streak with a 3-pointer of his own at 8:57, but GC wasn't finished.
The Quakers answered Gonzalez' 3-ball with another run, this one 8-0, to expand their lead to 25-9 with four minutes to play in the opening stanza.
From this point on, Guilford held at least a 12-point lead.
Junior Evan Bates got the Hornets to that 12-point deficit by opening the second half with one of his three 3-pointers on the day only to see GC the next five points and 10 of the next 15 to keep the pressure on its hosts.
The lead reached 27 before Shenandoah scored 19 of the final 29 points of the contest to provide the final margin.
Senior Malcolm Clark had a co-game-high 17 points to go along with 11 rebounds. The double-double is his fourth of the season.
Bates had 10 points in his fourth start of the year.
Alston Thompson had 17 points, Carson Long 12 and Dominique Henderson 11 for Guilford.
The Quakers had a 45-34 advantage on the glass and scored 16 points off of 13 SU turnovers.