Kyle Brindza kicked three second-half field goals, the go-ahead kick from 25 yards with 3:03 remaining. He tied a Notre Dame record with a 53-yarder that matched the longest in a college game at the $1.2-billion home of the Dallas Cowboys.
It was the second win in Texas in the five-year Shamrock run of home games on the road for the Irish (4-2), starting with a victory over Washington State in San Antonio in 2009.
Taylor Kelly threw for 362 yards and three scores for the Sun Devils (3-2), who missed on a chance to become the first team to beat USC and Notre Dame in consecutive weeks.
T.J. Jones had eight catches for 135 yards, including a pair of first-down catches on the drive to the winning field goal. Cam McDaniel, who went to school in nearby Coppell, had four straight carries for 32 yards to get Notre Dame in field-goal range.
The Irish clinched the win when Dan Fox, who recovered a fumble to set up a touchdown, returned Kelly's second intercepted pass 14 yards for a touchdown with 1:08 remaining.
The Sun Devils pulled within 37-24 on Kelly's third touchdown — a 16-yarder to Marion Grice with 11 seconds left — but Jones recovered an onside kick.
Notre Dame, one of the best in the country at rushing the passer last season but statistically one of the worst this season, found its form.
The Irish pressured Kelly throughout, and Prince Shembo had a key sack on the first play after Notre Dame went ahead.