The wild-card victory advances Baltimore to the next round of the playoffs in Indianapolis Saturday against the top-seeded Colts.
The Ravens ran up a 24-0 lead in the first quarter and benefited in the surprisingly one-sided contest from four turnovers by New England quarterback Tom Brady.
Rice, who also scored on a 1-yard touchdown run, rushed for 159 yards.
Other Baltimore touchdowns came on runs of 1 yard by LeRon McClain and 3 yards by Willis McGahee and the Ravens' Billy Cundiff kicked field goals from 27 and 23 yards.
New England, which had not lost a playoff game on its home field in more than 30 years, scored on two short Brady passes to rookie Julian Edelman -- for 6 yards in the second quarter and 1 yard in the third.
Brady was intercepted three times and lost a fumble.
The veteran New England quarterback ended up with 154 yards passing on 23 completions in 42 attempts.
The Ravens' Joe Flacco completed 4-of-10 passes for just 32 yards.
Swim Week Miami Beach 2014 [PHOTOS]