John Kinder drove Stony Brook (1-3) into the red zone, but Tillman shifted momentum with his pick six with 4:42 left in the third quarter.
North Dakota continued to stall Stony Brook's ensuing drives, forcing two fumbles, two punts and stuffing a fourth-down attempt.
Kinder was 12 of 18 for 172 yards. Will Tye had five receptions for 103 yards.
The Seawolves outgained UND 221-145 in total yards, but their three turnovers proved costly.