Stafford completed 16 of 26 passes for 221 yards and a touchdown.
Williams rushed for 89 yards and two touchdowns in 24 carries. He caught two passes for 27 yards and a touchdown.
San Francisco quarterback Brock Purdy tossed three touchdown passes to receiver Jauan Jennings, but it was not enough to hold off the Rams.
It was an important victory for a Rams team that is without injured receiver Cooper Kupp, who is out indefinitely, and receiver Puka Nacua, offensive linemen Steve Avila, Joe Noteboom and Jonah Jackson and defensive backs Darious Williams and John Johnson III are on injured reserve.
Kyren Williams scored his third touchdown of the game on a four-yard carry as the Rams tie the 49ers late in the fourth quarter in what has been a remarkable turnaround for the team.
Stafford connected with Tutu Atwell on a spectacular 50-yard pass to open the drive and set up the touchdown run three plays later.
San Francisco kicker Jake Moody missed a 55-yard field-goal attempt to keep it a one-touchdown game late in the fourth quarter.
The Rams managed to put the brakes on San Francisco’s seven-play, 33-yard drive by shutting down the passing lanes for Brock Purdy on third down.
The Rams will get good field position at their 45-yard line.
