Jeff Kari had 14 points for Lafayette (6-11, 2-1 Patriot League), which sank 27 of 30 free throws.
The Leopards went on a 9-0 first-half run to take a 32-24 lead. Kina hit a free throw to narrow the margin to 36-34 with just over two minutes remaining, but a 3-pointer by Ben Wheeler in the final seconds gave Lafayette a 43-38 lead at the break.
Foul shots and a layup by Kari in the opening minutes of the second half helped Lafayette extend its lead to 50-38 with 17:29 remaining. Kina cut the deficit to 58-55 with a three-point play and made it a one-point game 2 1/2 minutes later, but Ryan Willen hit a 3-pointer and Kari hit a foul shot to make it 64-59 with 6:36 remaining.