The Generals (5-7, 1-2) scored the game's next 22 points and held SU scoreless for a span of 8:46 to take the lead for good.
Junior Kaimonne Douglas finally snapped the Hornets scoreless streak with a jumper at 3:23, but the damage was done.
W&L held a 20-point lead following Douglas' bucket and never gave up the lead again.
Shenandoah continued to battle, scoring 10 of the final 13 points of the half and nine of the initial 12 points in the second, but would get no closer than seven points.
SU reached that seven-point deficit following a Gabriel Gonzalez layup at 14:12 of the second only to see the Generals reel off the game's next eight points in just 98 seconds to push their advantage back out to 15.
The lead remained in double-digits the rest of the way.
Douglas and Gonzalez, who both came off the bench, shared team-high scoring honors with Malcolm Clark. All three men had 11 points.
Clark and Gonzalez each pulled down a team-high six rebounds.
Clayton Murtha had 26 points and Devin Kearns 20 for the hosts.
Washington & Lee shot 45 percent, made nine of its 22 attempts from beyond the arc and grabbed 37 of the game's 68 rebounds.
SU shot 34 percent from the field and 88 percent from the line.