Senior Megan Rahn clinched the game for Meredith (4-9, 2-5 USA South) by draining a pair of free throws with four seconds remaining.
Shenandoah (5-9, 2-5) got the ball into its frontcourt on the ensuing inbounds, but Sam Akers' running jumper glanced off the rim as time expired.
Rahn's two free throws capped a comeback from 15 points down for the Avenging Angels.
SU led 48-33 following a Nicole Gilbertson jump shot with 16:25 remaining, but could only watch as MC staged the furious comeback.
The Angels scored the game's next 11 points to make it 48-44 with 10:33 remaining, and after Shenandoah bought itself some breathing room with an Akers 3-pointer and an Arianna Beard baseline jumper, staged another run.
This 6-0 spurt tied the game at 53-53 with exactly six minutes left.
The Hornets answered with consecutive jumpers from Gilbertson and Holly Chittenden before Rahn gave the hosts their first lead by backing up a Bryana Holmes '3' with four consecutive free throws.
This advantage eventually was pushed to four points on two different occasions, the last with 32 seconds left, but Akers kept Shenandoah alive by sandwiching two 3-pointers around two Holmes free throws.
Rahn was then fouled in the lane with four seconds left, setting the stage for the final play of the contest.
Gilbertson led SU with 21 points while Akers and Mandy Johnston both had 16.
Gilbertson also had a game-high 13 rebounds.
Shenandoah owned a 59-45 advantage on the glass.
SU is back in action on Wednesday at 5:30 in Newport News against Christopher Newport University. The game is the opener of a doubleheader with the Shenandoah men.