Wells broke LeShon Johnson's 15-year-old team mark of 214 rushing yards in a single game with a 14-yard run late in the fourth quarter.
Arizona's Patrick Peterson, meanwhile, tied an NFL record with his fourth punt-return touchdown of the season, running back a kick 80 yards for a score as the Cardinals logged their seventh straight win in St. Louis.
Larry Fitzgerald made three grabs for 55 yards in the win.
The Rams (2-9) were led by Sam Bradford, who completed 17-of-31 passes for 203 yards and a touchdown.
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance
Exploding whale video goes viral on Internet