SU falls to seventh place due to the loss coupled with an Averett win at Mary Baldwin, and will have to face co-champion and No. 2 seed Christopher Newport in Tuesday's quarterfinal round of the USA South Conference Tournament.
This game is scheduled for a 7 p.m. start at CNU's Freeman Center.
Greensboro, which shot 45 percent (14 for 31) in the first half, seized control of the contest with a 21-2 run midway through the opening 20 minutes.
With Shenandoah on top 10-6 following an Abby Gallagher jumper at the 16:38 mark, GC ripped off 21 of the next 23 points in a span of 8:16 to take a 27-12 with 7:29 remaining.
SU would get no closer than 11 points the rest of the way.
Trailing 36-23 at the break, the Hornets would generally match the Pride for the opening nine minutes of the second before GC finally sealed the contest with a 10-5 run from the 10:04 to 7:07 marks of the second.
The Pride turned their 13-point advantage into an 18-point bulge thanks to this run and coasted home to the 16-point victory.
Gabrielle Clarke had a team-high rebounds.
Danielle Duncan, a pre-season All-America, had 25 points for the victors.