Hancock, the hero in fourth-seeded Louisville's (31-5) second round win over Manhattan, made four 3-pointers in the triumph. He scored eight of the Cardinals' final 11 points last round.
Louisville, which has reached the Final Four each of the past two seasons and won the National Championship in 2013, awaits the winner of Sunday's clash between Wichita State and Kentucky.
The Cardinals have met both schools in the tournament the past two seasons, falling to eventual champ Kentucky in 2012 and taking out the Shockers to reach the finals last year.
Russ Smith and Chris Jones each netted 11 points while Montrezl Harrell donated 10 points with 11 rebounds for the Cards.
The Billikens (27-7) got 16 points and 10 boards from Dwayne Evans and 15 points with seven assists from Jordair Jett as both seniors enjoyed their final collegiate game.
Saint Louis missed all 15 of its 3-point tries and shot just 39.6 percent from the floor.