Crowder had nine points in an early run that gave the Golden Eagles to an 18-5 lead 5 minutes into the game.
With fresh memories of BYU's record-setting comeback from 25 points down in the tournament first round versus Iona Tuesday, however, the Marquette lead didn't seem safe.
But the Eagles were able to stem each BYU (26-9) attempt to get back into the game.
Marquette (26-7) moves into the third round for a game against sixth-seeded Murray State (31-1). The Racers opened Thursday play in Louisville with a 58-41 victory over Colorado State.
Marquette was up 15 at the half but the Cougars, also remembering their comeback, kept fighting. They closed the deficit to single digits more than once but Marquette would again pull away.
Crowder added five steals and four assists to his impressive points and rebounds totals Darius Johnson-Odom had 20 points and Davante Gardner 15 for the Golden Eagles.
Brandon Davies had 19 points in leading the BYU attack. Noah Hartsock added 15 points and Craig Cusick 12 for the Cougars.