The Wolf Pack (7-15, 3-7 Mountain West) ended a seven-game losing streak while the Spartans (2-21, 0-11) lost their 13th straight.
Both teams had numerous chances in the final two minutes after Darryl Gaynor II made a layup to pull San Jose within 54-53.
West responded with a layup at 1:34 but in the final 1:05 Nevada made just 2 of 8 free throws.
After Gaynor's bucket the Spartans missed three shots, two free throws and had a turnover. Gaynor scored with four seconds left to make it 59-57 before Criswell was fouled. He made the first free throw and then snagged the rebound that sealed the game.
Gaynor led San Jose with 25 points.