Coach Rick Pitino added this title to the one he won at Kentucky in 1996 and is the first coach to win a championship at two schools. Earlier in the day, Pitino was elected to the Naismith Memorial Hall of Fame.
Hancock scored 22 points and Peyton Siva had 18 for the Cardinals (35-5), who trailed by 12 late in the first half before rallying for the school’s third national title.
Trey Burke had 24 points for Michigan (31-8), which was in the final for the first time since the Fab Five led the Wolverines there in 1993. Little-used freshman Spike Albrecht added 17 points.
But the celebration belonged to the Cardinals, who added this to a Sugar Bowl victory this year and also have their women’s team in Tuesday’s national final against Connecticut.
Chane Behanan scored nine quick points early in the second half to help Louisville take the lead after trailing by double digits.
Behanan finished with 15 points and 13 rebounds, including eight on the offensive glass.
Albrecht came in for Burke and made his first four 3-point attempts, scoring all his points in the opening half. Albrecht finally missed with a little more than 11 minutes left; he was still 9-for-10 from long range for the tournament.
Hancock made all four of his 3-pointers to start a 14-1 run for Louisville that briefly gave the Cardinals a one-point lead late in the first half after they trailed by 12.
Michigan’s Glenn Robinson III made two free throws with 2 seconds left to give the Wolverines the lead at the half but Louisville led by as many as five early in the second.
The Cardinals came in having won six games this season after trailing by 10 or more, including Saturday night’s semifinals, when they beat Wichita State 72-68 after also falling behind by 12.
It was a scintillating final act of a season that has been more of a grind, with scoring at its lowest (67.49 points per team) since 1951-52 and shooting at its worst (43.3 percent) since 1964-65.
The 131.2-points-per-game average during March Madness is the lowest since the 3-point line was brought to the game in 1987, though the teams had surpassed that with 5:30 left.
Sitting on the bench with the Cardinals was sophomore guard Kevin Ware, the team’s inspiration since snapping his tibia in the regional final last weekend.
Needing a pickup without Ware, Hancock led the scoring against Wichita State. And rarely used walk-on Tim Henderson made two key 3-pointers during the comeback.
Pitino, meanwhile, was working the sideline hours after being chosen for the Naismith Memorial Hall of Fame.
Russ Smith, the Louisville team leader who Pitino has nicknamed “Russdiculous” for some of his wild — and wildly effective — antics on the court, finished with nine points on 3-of-16 shooting.
Michigan topped Syracuse 61-56 on Saturday despite an off night from Burke, who finished with only seven points on 1-for-8 shooting.
Burke, a sophomore, seriously considered leaving for the NBA after last season but decided he had unfinished business left in Ann Arbor. He picked up the AP Player of the Year award, among others, and is now one victory away from the ultimate prize in college hoops.