Trist did it with 12-of-20 shooting from the field for the Leopards (12-8, 4-5 Patriot League). Bryce Scott added nine points, nine rebounds, five assists and four steals.
Colgate led 18-9 midway through the first period and was up 32-25 at the break.
Lafayette battled back in the second half with Monty Boykins hitting a 3-pointer to tie it up 42-42 and then Nick Linder sinking a jumper to put the Leopards ahead for the first time, 46-45, with 10:30 to play. Trist hit a jumper to make it 55-51 with 1:04 remaining and Linder went 4 of 4 from the line in the final seconds to clinch it for the Leopards.
Ethan Jacobs had 14 points and six rebounds for the Raiders (9-13, 6-3).