The Beavers (9-4), who won their fourth straight, became the first Pac-10 team to capture a bowl game this season. UCLA and Arizona State had previously dropped their post-season contests.
Bernard gained 176 yards on 38 carries and scored on a two-yard run in the second quarter to tie the game at 14-14.
Rodgers picked up 100 yards on the ground and caught a 14-yard scoring pass from Sean Canfield in the opening period. Rodgers then scooped up a fumble by Bernard at the Maryland one-yard line and carried it in for the go-ahead score with 10 seconds left in the third quarter.
The Beavers' defense took it from there, limiting Maryland's ground game to 38 yards on 23 carries.
Maryland's Chris Turner completed 17 of 29 throws for 201 yards and two touchdowns, but he was intercepted twice. The Terrapins wound up with a 6-7 record.