Notre Dame outplayed Kentucky (4-2) inside during the first half and held the Wildcats to a season-low 40 percent shooting for the game. Students rushed the floor after the Irish wrapped up their second win over the Wildcats in the past 13 meetings.
The senior captains of the top-ranked Notre Dame football team, linebacker Manti Te'o, defensive end Kapron Lewis-Moore, tight end Tyler Eifert and tackle Zack Martin, got a standing ovation when they were introduced at halftime.
Julius Mays led Kentucky with 16 points and Nerlens Noel had 10.
Two of Kentucky's heralded freshmen struggled. Archie Goodwin, who is averaging 19 points, was 1 of 7 shooting and finished with three points and Alex Polythress, who is averaging 18.4 points, had just one basket and was 1 of 3 from the free-throw line.
Cooley added 11 rebounds for the Irish, who outrebounded Kentucky 33-27. Noel and Goodwin each had seven rebounds.
After struggling early, the Irish made 9 of 10 shots during a 24-11 run at the end of the first half and Kentucky couldn't get any closer than 10 points in the second half.
Notre Dame led 36-25 at halftime. The lead was around 10 points when Cameron Biedscheid, who had 10 points, hit a 3-pointer to ignite a 10-0 run that included a 3-pointer by Grant and another jumper by Biedscheid and gave Notre Dame a 55-35 lead.
Kentucky used a 13-4 run to cut the lead to 59-48 on a dunk by Willie Cauley-Stein with 3:31 left.
The Irish, who struggled inside in their overtime loss to Saint Joseph's, outscored the Wildcats 20-12 inside in the first half, although the Wildcats evened it up in the second half.
Notre Dame wore black uniforms with stitched green letters, and the crowd wore black in support of the team.