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.
Former Michigan point guard Spike Albrecht will play for Purdue as a graduate transfer next season.
Only six major-conference teams have failed to win an NCAA tournament game since the turn of the century. When will each program snap the streak?
Bruce Weber's Kansas State team earned a share of the Big 12 title three years ago, but a lot has changed since then and the pressure is on.