The Panthers (2-3) outgained the Owls 320-60 in the first half and 479-277 overall in snapping a three-game losing streak. Browne was 14 of 16 for 247 yards and two touchdowns prior to intermission. He finished 28 of 32.
Running back Chawntez Moss recorded two touchdowns -- one rushing and one receiving -- for Pitt.
Rice sophomore quarterback Jackson Tyner was 15 of 32 for 222 yards with a touchdown and three interceptions.
The Owls (1-4) entered the game 118th nationally in total offense among 129 FBS teams at 292 yards per game.
The Panthers raced to a 21-0 lead after one quarter, outgaining Rice 201-34 in the period.
Browne had plenty of time to connect with Moss for a 48-yard touchdown and found wide receiver Jester Weah all alone for a 55-yard score. Running back Qadree Ollison capped the outburst with a 10-yard TD run with 1:13 left in the first.
Moss fumbled on third-and-goal from the 1, denying Pitt a scoring opportunity on its fourth possession. Moss atoned for his mistake on the next drive when he scored from the 1 with 2:02 left in the first half to make it 28-0.
The Owls avoided being shut out for the first time since 2000 as Haden Tobola kicked a 23-yard field goal on the opening drive of the second half. Rice made it 28-10 when Tyner connected with running back Austin Walter for a 70-yard touchdown later in the third quarter.
Browne's 1-yard touchdown pass to running back Darrin Hall restored the Panthers' 25-point lead with 12:22 remaining.