Muscala finished with 12 points and 10 boards while Bryan Johnson tallied 17 points, eight rebounds and six assists for the Bison (20-4, 7-1 Patriot League), who won despite not scoring a basket in the final two minutes.
Army (10-13, 3-5) trailed by as much as seven, 35-28, in the second half before cutting the deficit to 52-50 with 4:13 left. But Ayers knocked down a 3-pointer and Johnson converted a trey and a jumper on back-to-back possessions to put Bucknell ahead 60-54.
The Bison went scoreless from that point as Army drew to within two, 60-58, with 1:57 remaining but missed three jumpers in the final minute as Bucknell held on.
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Duke and Cincinnati, 2016 NCAA tournament teams, highlight the eight-team field for the Naismith Memorial Basketball Hall of Fame Tip-Off Tournament.