Ford gave Cornell (2-0, 1-0 Ivy League) a lead it never surrendered on a quarterback keeper 5 minutes, 45 seconds into the game. Barbour expanded the lead early in the second quarter on a run to the left on third-and-goal.
Gio Christodoulou scored for Yale (1-1, 0-1) on a 71-yard punt return late in the first half, but Brad Greenway expanded Cornell's lead to 17-7 with a 21-yard field goal early in the third quarter.
Yale committed four fumbles in the first 15:08 of the second half, losing three, but was able to drive late to close the gap to three points. Jarrett Drake caught a pass from Ryan Fodor from 7 yards out with 58 seconds remaining on the only drive where the Bulldogs ran a play from scrimmage inside the Cornell 25.
But the Big Red's Jesse Baker recovered the ensuing onside kick and iced the game.
The loss was Yale's fourth in its last 22 league games, and its first on the road since Oct. 22, 2005.
Taylor Zalewski 27 yd FG MISSED
Joshua Dobbs pass complete to Von Pearson for 5 yds for a TD
Joe Williams rushes for 187 yards and a touchdown in Utah's 20-14 victory over Colorado.
Cody Kessler pass complete to Taylor McNamara for 7 yds for a TD
Jack Allen run for 9 yds for a TD
Jalen Hurd run for 48 yds to the Vandy 9 for a 1ST down