Dixon's run gave the 49ers a 34-13 lead with 6:30 remaining in the fourth quarter, and it indeed ended up clinching the NFC's No. 2 seed and a first-round playoff bye for San Francisco (13-3).
But St. Louis stormed back after that with two touchdowns made possible by an onside kick recovery.
The Rams were set to tie the game, holding the ball near midfield with about 4 minutes to play, but backup quarterback Kellen Clemens hurt his ankle and St. Louis (2-14) turned the ball over on downs.
That allowed the NFC West champions to barely hang on for a key victory.