The Rams were 26 of 37 from the line (70 percent) for the game.
The game began more than 30 minutes late because the referees were stuck in traffic caused by a standoff that closed I-70. One of the three scheduled officials and an official from the women's game, which had just finished, started the game.
West Virginia State (2-7, 2-3) used its grinding, guard-oriented offense and space-eating zone defenses to slow the game and take an early 14-6 lead. The Rams (5-6, 3-2) made a comeback by extending pressure defensively to change the tempo of the game.
"It was a frustrating game for us," said Alexander, who defeated State for the first time in four tries. "We were never really able to get everything smooth and comfortable. Then when they finally tied it, we would bend but we didn't break."
With State shutting down forward Richie Sutherland, and Rashad Crutchfield hampered by early foul trouble, Shepherd got a needed spark off the bench from Ron Fitzpatrick.
The freshman point guard scored all 10 of his points in the final 11 minutes in the first half as Shepherd took a 37-32 lead at halftime.
Sutherland didn't take his first shot until the 13:38 mark of the second half and Crutchfield was ineffective with three first-half fouls.
Shepherd took a 41-32 lead to open the second half before the Yellow Jackets ran off a 13-4 run to tie the game at 45.
Then the Rams started the procession to the foul line.
West Virginia State's Rahim Walls led all scorers with 18 points.
Shepherd placed four players in double figures, led by Duane Harris, who had 15 points.