The Generals (3-1, 1-0 ODAC) had a 19-rebound edge (47-28) over SU to prevent the Hornets (2-3, 0-1) from winning in their first-ever ODAC game.
W&L used that rebounding edge, and the height advantage that keyed the rebounding edge, to outscore Shenandoah 42-26 in the paint and record 14 of the game's 21 second-chance points.
Washington & Lee was also 20 of 28 from the line to the Hornets 3 of 6.
The two teams traded the lead eight times and were tied on seven other occasions during the contest; the Generals took the lead for with 7:07 to play as J.D. Ey canned a jumper in the paint.
Ey's turnaround jumper, one of a game-high 10 buckets he had on the day, started an 8-2 run for W&L that gave the visitors a 60-54 lead with 3:57 remaining.
Shenandoah was able to cut the deficit to three, 66-63, on a Jared Carithers fastbreak layup with five seconds remaining, but Kevin Gill hit both free throws for Washington & Lee with three seconds left to provide the final margin of victory.
SU shot 38.5 percent (25 of 65) for the game and was 10 of 24 (41.7 percent) from behind the arc.
Ey led all players with 22 points and 12 boards.
Shenandoah is back in action on Monday night at 7 p.m. in a non-league home contest against Frostburg State.