Smith scored 10 of his 21 points in the second half and Hancock added 11 of his 20 after the break -- including two late 3-pointers -- as the Cardinals (34-5) erased a 12-point deficit.
Tim Henderson began the late surge with a pair of 3-pointers and Louisville went on a 12-3 run, grabbing the lead for good in its quest for its first NCAA championship since 1986.
Chane Behanan provided 10 points and nine rebounds for the Cardinals, who will face fourth-seeded Michigan in Monday's title tilt.
The Wolverines bested Syracuse 72-68 in Saturday's second national semifinal.
Cleanthony Early paced the ninth-seeded Shockers (30-9) with 24 points and 10 rebounds.
Carl Hall (13 points, five rebounds) and Ron Baker (11, eight) also reached double figures for Wichita State.