Birch scored 14 of his points in the second half, hitting all seven of his shots from the field and adding five rebounds. Ashton Gibbs, the Big East preseason player of the year, added 15 points for the Panthers.
Gibbs scored eight of Pitt's 11 points in a 4-minute span near the end of the first half.
The Panthers held La Roche to 25 percent shooting and forced 21 Redhawks turnovers. Mike Dixon led Division III La Roche with 14 points, scoring the Redhawks' first seven of the game.
Former La Roche head coach Scott Lang was honored in a pregame ceremony. Lang died at age 41 last December after he suffered a heart attack and collapsed at center court during a practice.