The Packers were threatening to win or force overtime with less than 30 seconds left, but St. Louis' Jerametrius Butler recovered Brett Favre's fumble deep in Rams territory.
Marc Bulger passed for 220 yards and two touchdowns, Steven Jackson rushed for 98 yards on 23 carries and Torry Holt had a touchdown on three receptions for 40 yards for the Rams (4-1), who have won three straight games.
For the Packers (1-4), Favre was 22-of-39 for 220 yards and a touchdown. Noah Herron rushed for 106 yards on 20 carries and Greg Jennings had one touchdown on five catches for 105 yards.
The only points scored by the Rams in the second half came on field goals by Wilkins, one in the third quarter, and two in the fourth.