Now the Fighting Irish are headed to the regional semifinals for the first time in 16 years.
Dan Miller matched a career high with 23 points and Notre Dame had 13 three-point baskets to move into the round of 16 with a 68-60 win over Illinois in the West Regional on Saturday.
"We were running and firing and I did not want to stop us because we were going for it," said Brey, who celebrated his 44th birthday with a big victory.
Notre Dame will travel to Anaheim to play top-seeded Arizona, which beat Gonzaga 96-95 in double overtime.
Chris Thomas had 17 points for the fifth-seeded Irish, who had not advanced this far in the NCAAs since 1987 under coach Digger Phelps. That year, they were eliminated in the regional semifinals by North Carolina.
"This is huge for our program," Brey said. "In the summer we talked about playing on the second weekend. I'm happy this group set a goal and achieved it."
It was a disappointing second-round exit for fourth-seeded Illinois (25-7) -- the Big Ten tournament champion. Conference player of the year Brian Cook had 19 points and 16 rebounds.
The Fighting Illini trailed by 13 at halftime but cut it to six with 1:45 left after Deron Williams' tip in. They didn't score another basket.
Williams went end-to-end after a steal but missed the layup, and Chris Quinn's two free throws with 27 seconds left sealed the victory.
The Irish (24-9) lost in the second round the last two years -- without Miller, a transfer from Maryland.
He made five of seven three-point shots and Notre Dame was 13 for 24 from behind the arc. The Irish topped their previous tournament high of 10 three-point baskets, set last year against Charlotte.
"When the big guys played off me, I shot it. When they came up on me, I tried to drive by them," Miller said. "When I got that stretch going, they were playing off me so I just pulled the trigger on them."
The Irish came out shooting three-pointers on almost every possession. Their first three field goals were threes and they started six for 11 from long range. Miller made his first five three-pointers, and the Irish went 11 for 16 in the half. Thomas and Matt Carroll each made three from behind the arc.
Carroll, playing on a sprained left ankle, scored 11 points. Torin Francis grabbed 14 rebounds for Notre Dame.
"The way they came out and played in the first half, no one would have been able to beat them," Illinois Coach Bill Self said. "We got a lot of looks. They just didn't fall today."
Illinois never led and had trouble getting into its offense early. Cook missed five of his first six shots, and the Illini shot only 38%.
Notre Dame built a 47-34 lead but struggled to start the second half. The Irish missed seven of eight shots, allowing Illinois to pull within eight.
Thomas and Miller combined for eight straight points midway through the half to push the lead back to 14.