American (12-10, 5-5 Patriot League) shot just 28.6 percent (6 of 21) in the first half and trailed 23-18 at the break and Malcolm Miller's layup with 16:51 to play gave Holy Cross a 30-20 lead.
A 12-4 run pulled American within two about five minutes later before a 3-pointer by Reed sparked an 11-2 spurt which made it 50-45 with two minutes to play.
Miller hit two free throws with 16 seconds remaining to pull Holy Cross (8-12, 3-7) within 52-50, but Charlie Jones made two at the line and Gardner came up with a steal and hit 1 of 2 free throws six seconds later to seal it.
Miller led Holy Cross with 19 points.
American shot a season-high 58.8 percent from 3-point range and hit 14 of 25 (56 percent) second-half field goals.