Dartmouth (2-3) snapped a two-game losing streak, while Colgate (4-2) dropped its second straight. Michael Giovacchini added 14 points for the Big Green, who shot 54 percent from the field and 45 percent from 3-point range.
The first half saw three lead changes and the teams were tied 34-34 at the break.
Colgate held an eight-point lead, 47-39, with 13:54, before Dartmouth rallied to tie 52-52 two minutes later.
The Raiders went up 63-62 with 4:42 left on Roemer's jumper, before Dartmouth scored the next six points to take the lead for good. Mosley had a pair of baskets and Brandon Ware added a basket in the decisive run.