McCarney, who also threw an interception, connected with Ryne Morrison on a 34-yard touchdown to open the scoring for Colgate (5-6, 2-4 Patriot League). Bucknell responded with field goals of 19 and 33 yards by Drew Orth to pull within 7-6 going into halftime.
But it was all Raiders in the second half, as McCarney busted a 50-yard rushing score in the third quarter and Vinnie Nicosia returned an interception 79 yards for a score in the fourth.
Tim Lauletta finished with 166 passing yards and two interceptions for the Bison (6-5, 3-3).
Bucknell outgained Colgate 307-259 on total offense, but lost two turnovers compared to just one for the Raiders.