The Black Knights (10-11, 3-3 Patriot League), who won two consecutive games for the first time since Dec. 22, trailed 20-13 when Ellis hit three free throws at the 9:20 mark. That sparked a 25-14 run to close the first half.
Larry Toomey's 3-pointer extended Army's lead to 41-34 after the break. The Crusaders closed to 44-42 on a pair of Phil Beans free throws, but Cartavious Kincade and Wilson answered with layups and Ellis hit two more foul shots.
The Crusaders climbed back within four points, the last time at 68-64, before Wilson, in his second career start, scored six straight points as part of a 10-0 spurt.
Justin Burrell's 14 points led Holy Cross (10-11, 2-4), which has lost three straight.
San Diego State's student section, "The Show," has been known to harass opponents. Does it make Viejas Arena the Mountain West's most difficult venue?
Which venue in the Mountain West is the toughest place to steal a win? Cast your vote.
Who can challenge DeAndre Ayton for No. 1 in the ESPN 100? It's one of the issues worth watching as we exit basketball recruiting's biggest month.