Stafford made up for a shaky game by leading an 80-yard, nine-play game-winning possession that included three passes of at least 18 yards.
Sam Bradford directed a go-ahead drive that set up Greg Zuerlein's 46-yard field goal and put the Rams ahead 23-20 with 1:55 left. But coach Jeff Fisher's debut ended with a loss because the Rams could not shut down Stafford in the end.
Stafford had three interceptions before halftime for the first time in his four seasons. The Rams scored 13 points off Stafford's turnovers, including Cortland Finnegan's 31-yard return for a TD that gave them a 13-7 lead late in the first half.