Guilford (16-5, 8-4 ODAC) turned a two-point, 30-28, advantage into a 40-30 lead with 12:53 to play on the strength of a 10-2 run.
Freshman Jimi Starks finally ended the drought for the Hornets (3-18, 0-12) with a jumper at 12:14, but GC would hold the lead for the remainder of the contest.
Shenandoah was able to cut the deficit to five points with 7:47 left before the Quakers reeled off seven straight points to seal the victory.
The two teams traded the lead four times and were tied on five other occasions. The Hornets last lead was 21-20 with 3:23 remaining in the first half.
Josh Pittman paced the victors with a game-high 28 points to go along with 10 rebounds. Pittman also was 10 for 10 from the line.
Three of the five SU starters hit in double figures, led by Jared Carithers' 17.
Guilford had a 46-25 advantage on the glass which led to a 22-4 bulge in points in the paint.
SU hosts Bridgewater on Wednesday in a 7:00 ODAC contest.