Trailing 28-24 with 2:52 to play, Sacred Heart recovered a fumble on their own 35 for a chance at a game-winning drive, but were stopped on downs and the Dukes (7-3, 4-1 Northeast Conference) ran out the clock after Hines converted on third-and-1.
Parr scored on a 4-yard run three plays after Jassir Jordan returned the opening kickoff 76 yards. Hines (31 carries) capped the Dukes' second drive with a 32-yard run. Hines gained 232 yards on 33 carries in Duquesne's 47-30 win over Wagner last week.
Parr, 11 of 16 for 126 yards passing, hit Taylor on a 36-yard TD pass for a 21-7 Duquesne halftime lead. Taylor caught five passes for a career-high 86 yards. Daquan Worley scored on a 1-yard run in the third.
The Pioneers (6-4, 4-1) rallied in the second half, with Jordan Meachum (174 yards on 29 carries) scoring on a 1-yard run and Kevin Duke on a 3-yard run. Noah Gettman kicked a 24-yard field goal, but Sacred Heart couldn't convert on the final drive. Julius Chestnut gained 131 yards on 10 carries.