"I was just trying to make a play," said Muscala, who credited teammate Steven Kaspar for tipping him the ball in the closing sequence.
Bucknell began the night tied for first in the Patriot League at 4-1 with Lehigh, which played won Wednesday at Navy.
The Bison made just 11 of 24 free throws and hit just one of 10 shots from 3-point range but came back for an eight-point deficit with 5:54 left in the game.
"We showed unbelievable grit and resilence," said Bucknell coach Dave Paulsen. "It was a miracle to come back" and win.
American took a 50-44 lead with 6:48 left in the game with two free throws by Munoz. The Eagles expanded the lead to 52-44 on an offensive rebound and putback by Tony Wroblicky before Bucknell battled back.