Hidalgo had eight assists and the nation's leader in steals had six to bring her total in the first four games on her career to 27. Westbeld had three 3s and eight rebounds.
The Irish were without leading scorer Sonia Citron (20.3), who injured a knee in Wednesday's win over Northwestern. Sophomore Cass Prosper had eight points in her first career start. Citron is expected to miss two weeks with a sprained knee.
KK Bransford added 11 points and six offensive rebounds off the bench for Notre Dame (3-1).
Genesis Bryant had 31 points for the Illini (2-2), Adalia McKenzie had 17 with eight rebounds and Makira Cook 14 points.
The Illini were within one three minutes before halftime before the Irish reeled off the final nine points of the second quarter to lead 37-27. Westbeld started it with a three-point play and Anna DeWolfe contributed a 3-pointer.
Westbeld had 15 points at the break, as did Bryant.
Notre Dame used a 9-0 run early in the second half, with Bransford scoring five, to open a 49-33 lead and pushed it up to 19 before taking a 61-45 lead into the fourth quarter.
Bransford hit a 3-pointer in the first minutes of the fourth quarter to make it a 20-point game and Hidalgo had a layup to make it 70-50 with 6:44 to play
Last year the Irish beat Cal in St. Louis in the first Shamrock Classic, which was also the first women's game on NBC.
Notre Dame returns home to play Chicago State on Tuesday. The Illini are off until the Nov. 26 when they play host to Canisius.
__ Get alerts and updates on AP Top 25 basketball throughout the season. Sign up here ___ AP women’s college basketball: https://apnews.com/hub/ap-top-25-womens-college-basketball-poll and https://apnews.com/hub/womens-college-basketball