Muscala finished with 13 points and 11 rebounds and Joe Willman made 4 of 5 shots en route to 10 points for the Bison, who shot a season-high 62 percent (28 of 45) from the field.
Bucknell (13-2) held a 57-52 advantage with 5:53 left before Johnson hit a 3-pointer, sparking a 13-2 run over the next five minutes for the Bison. Johnson made two treys and Ayers had four points during the run.
The Bison, who equaled their best 15-game start in program history with the win, held a 34-24 rebounding advantage and dished out a season-high 20 assists.
Cornell's (6-9) last basket came on a Josh Figini layup with 2:24 remaining.
Figini led the Big Red with 15 points.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.