Dube's touchdown catch was the 34th of his career, moving him past Ed Pricolo into second place on the school's all-time list for receiving touchdowns.
Noel completed 15 of 22 passes for 270 yards and two scores. Nate Chavious added 76 yards rushing and a touchdown for Sacred Heart (4-2).
The Pioneers jumped out to a 10-0 lead and led 17-6 at the half.
Josh Sweet led Cornell (0-5) with 80 yards rushing on 22 carries and one touchdown, a 3-yard second quarter run that provided the Big Red with their only points.
Robert Somborn finished with 196 yards passing and an interception for Cornell.