Kyle Brindza kicked a go-ahead, 25-yard field goal with 3:03 left, putting Notre Dame ahead at 30-27 after Rees led the Fighting Irish (4-2) on a 10-play, 56-yard drive.
Mathias Farley picked off ASU's Taylor Kelly on the next series and Dan Fox later sealed the victory with an interception and 14-yard return for a score with 1:16 left.
Rees completed 17-of-38 passes for 279 yards.
Prince Shembo keyed Notre Dame's defensive effort with three sacks.
T.J. Jones hauled down eight passes for 135 yards and a score for the Irish.
The Sun Devils (3-2) lost despite a 362-yard, three-touchdown performance from Kelly, who surrendered the two late pick-offs on 33-of-47 efficiency.
Jaelen Strong made eight grabs for 136 yards and a TD for ASU.