Providence looked ready from the start, dumping the ball inside Notre Dame's zone defense and pounding the offensive glass.
"I just thought we played at such a high level," Cooley said. "I just thought we played with such great confidence, and it's because of what we did defensively." Bryce Cotton, the Big East scoring leader, had 19 points and LaDontae Henton 13 for the Friars (14-11, 6-7).
It was Providence's second win over a ranked team in 10 days following a 54-50 victory over then-No. 17 Cincinnati on Feb. 6.
"I think they are the most underrated team in our league, quite frankly," Irish coach Mike Brey said. "They're really hard to guard. I think Ed's done a fabulous job with them. I don't know if it was as much about us not playing great as it was them really playing well. When Batts is doing that inside, he's a pro. It's almost impossible to stop him."
The Friars held the Irish to 39.3 percent shooting, outrebounded them 43-32 and had 20 assists on their 29 baskets.
Notre Dame, which had played three overtime games in its previous four — winning all of them — was continually beat down the floor for easy baskets. It was such an easy game for the Friars that Cooley was even joking about some bad shots by Council.
"I think he was a 3 away from a triple-double," Cooley said. "I was wondering why he kept heaving up bad shots." Batts had 14 of his points in the opening half on 7-of-9 shooting.
"Our chemistry is great," he said. "I don't see a lot of teams that can beat us with the defense we play."
Council also had 11 rebounds and seven points. His 671 assists surpassed the 662 of Ernie DiGregorio from 1970-73. Council needs two assists to match the Big East record of 426 set by Syracuse's Sherman Douglas from 1985-89.
Jack Cooley led Notre Dame with 12 points and 10 rebounds, and Tom Knight and Garrick Sherman each scored 11. It was just the second loss in seven games for the Fighting Irish (20-6, 8-5).
The Friars led by eight points at halftime and increased their lead to 36-26 on the first possession of the second half when Batts made a one-handed baseline flip. They improved to 44-31 on Cotton's 3-pointer from the left corner with 17:21 to play.
"I was disappointed in our energy early in the game defensively, and they got confident, but I'm really impressed with them," Brey said.
Providence, which seemed to get nearly every loose ball in the early minutes of the second half, followed with a 15-6 run and opened a 56-39 lead on Cotton's corner jumper with just under 12 minutes to play. Henton keyed the run, scoring seven consecutive points.
After Sherman made a layup for the Irish, Providence used a 9-0 run for a 65-39 edge on Batts' jumper with 9:18 left. Council made a a pair of jumpers during the spree and Henton had a three-point play, coming off a hustle rebound and put-back.
"This is a game they were very ready for, and we came out a little flatter than we should have," Notre Dame guard/forward Pat Connaughton said.
Providence went over 5 minutes without scoring a point after opening its 17-point lead, but Notre Dame couldn't sustain any consistent offense. The Irish scored nine straight points, but it took them too long to make a serious run.