Hancock drained four of his five 3-pointers late in the first half as the Cardinals (35-5) overcame a 12-point deficit while Siva tallied 14 of his total after the break as Louisville pulled away down the stretch.
Siva's slam dunk off an assist from Hancock with 6:27 remaining gave the Cardinals a 67-62 lead and the Wolverines never got closer than 3 points thereafter.
Siva finished with six rebounds and five assists while Chane Behanan added 15 points and 12 boards for Louisville, which had previously won national championships in 1980 and 1986 under Coach Denny Crum.
Gorgui Dieng supplied eight points, eight rebounds, six assists and three blocks in the win.
Trey Burke scored 24 points for fourth-seeded Michigan (31-8), which fell short in a bid for its second national title and first since 1989.
Spike Albrecht went 4-of-5 from 3-point range en route to 17 points off the bench for the Wolverines.