Louisville raced to a 22-9 lead, opened a 23-point advantage at halftime and coasted to its fourth straight victory.
Blackshear came off the bench to score 16 points and had three field goals from long range. Hancock's four 3-pointers led to his 14 points.
Louisville (17-3, 6-1 American Athletic Conference) hit 12-of-23 from beyond the arc and forced 22 turnovers.
Chris Perry scored 20 points for South Florida (10-9, 1-5 ACC) and was the only member of the Bulls in double figures.
Louisville will not play again until Jan. 30, when the Cardinals will host conference-leading Cincinnati.