Richmond Aririguzoh added 15 points and Tosan Evbuomwan had 10 points and eight rebounds for the Tigers (1-5).
Princeton, trailing 43-39 at the break, opened the second half on a 28-7 run to go out front 67-50 after Llewellyn drained a 3-point jumper with 13:06 remaining in the game. Bucknell answered with a 16-3 run to close to 70-66 following Malachi Rhodes' dunk at the 8:23 mark of the second half.
The Tigers responded by draining 3s as Schwieger hit two straight and Drew Friberg added another for an 85-71 lead with 3:29 left.
The Tigers nailed 13 of 25 from deep (52%) hitting nine in the second half.
Jimmy Sotos had 20 points for the Bison (3-6). Avi Toomer added 19 points and seven rebounds. Andrew Funk had 14 points.