Alexander scored a career-high 26 points, including a go-ahead basket in OT, and sank 7 of 8 foul shots in the extra period, and Hamilton poured in a season-high 24 points for Holy Cross (9-12, 4-6 Patriot League), overcoming what had been a 12-point deficit.
Shawn Anderson led Navy (15-7, 6-3) with career-high 25 points and Tilman Dunbar added a season-high 24 as the Midshipmen lost for the 17th time in 18 games at Holy Cross' Hart Center.
Navy led from the game's second minute until Anthony Thompson tied it at 69-69 with 13 seconds left in regulation. The tying points were set up when Holy Cross fouled Edward Alade, who missed both.
Eric Green made Holy Cross' first two baskets of OT, and Alexander put the Crusaders ahead 76-73 with a 3-point play.