Skylar Diggins had 16 as the Fighting Irish (33-1) extended their school-record winning streak to 28 games and finished 13-0 on the road.
Notre Dame will next face 12th-seeded Kansas in Norfolk, Va., on Sunday.
McBride had 23 points in the first half as the Irish built a 12-point advantage. The lead reached 59-39 on Diggins' layup with 15:30 left as Notre Dame reached the round of 16 for the 11th time in 17 seasons.
Bethany Doolittle had 16 for Iowa (21-13), which went 0 for 11 from 3-point range and had 21 turnovers.