Jeff Wilkins kicked a 24-yard field goal as time expired in the fourth quarter, then won the game 4:38 into the extra session with a 49-yarder.
The Rams blew a 24-10 lead in the third quarter as the Cardinals scored 17 straight points to take the lead with 6:05 left on a 27-yard field goal by Neil Rackers. Rookie wide receiver Anquan Boldin, who caught six passes for 123 yards, had a pair of touchdowns as Arizona surged ahead.
Cardinals quarterback Jeff Blake completed 15-of-28 passes for 192 yards and a pair of touchdowns and two interceptions.
Bulger passed for 329 yards and one touchdown and Marshall Faulk rushed for 100 yards.