Mitola drained five 3-pointers on 9-for-15 shooting and was a perfect 6 of 6 at the line. He scored on a layup to forge a 46-all tie late in the game, and John Golden hit a 3 as Big Green (12-16, 5-9 Ivy) took the lead for keeps at 49-46.
The teams battled through nine ties and seven lead changes.
Justin Sears led the Bulldogs (15-13, 9-5) with 26 points on 7-of-10 shooting. The rest of the Bulldogs hit just 10 of 37 shots.
Yale entered the weekend with a chance to tie Harvard for the Ivy League title, but lost to the Crimson Friday, finishing second.
Dartmouth scored 21 points off 15 Yale turnovers.