Rice broke a pair of tackles en route to the end zone after receiving the Russell Wilson pass in the extra frame, capping a 12-play, 80-yard Seahawks drive. He finished with six catches for 99 yards, while Wilson completed 23-of-37 passes for 293 yards and two touchdowns for Seattle (7-5), which has won three of its last four games.
Golden Tate made five grabs for 96 yards with a score and Marshawn Lynch compiled 87 rushing yards and a touchdown on 19 carries for the Seahawks.
Chicago's Robbie Gould connected on a 46-yard field goal as regulation time expired to keep the contest alive, but the Bears (8-4) couldn't finish with a victory.
Jay Cutler went 17-of-26 through the air for 233 yards and two touchdowns for Chicago, which remained in a first-place tie with Green Bay atop the NFC North.