The Vikings (8-6) scored 10 of their 23 points in the second quarter off turnovers by Sam Bradford, including a 29-yard interception return by defensive end Everson Griffen that the Rams quarterback watched in disbelief from his knees.
They were up by 26 before Bradford, whose botched center snap also cost the Rams (6-7-1) a field goal in the second quarter, threw touchdown passes to Danny Amendola and Lance Kendricks in the fourth quarter.
The Vikings remained in the playoff picture while seriously damaging the Rams' postseason hopes. St. Louis had won three in a row to become a dark horse candidate for the playoffs.
Steven Jackson became the 15th player to rush for 10,000 yards for the Rams. He had 73 yards on just eight carries and has 909 yards on the year, keeping him in range of an eighth straight 1,000-yard season.
A moment of silence was observed for victims of the Connecticut elementary school shooting before the national anthem, with dozens of children wearing uniform jerseys holding hands with players in a circle extending from the 30-yard lines and centered on the Rams' logo at midfield.
In a tribute to the 26 victims, each team sent the players wearing the No. 26 jersey Rams running back Daryl Richardson and Vikings cornerback Antoine Winfield and they held hands with coaches Jeff Fisher and Leslie Frazier to form a smaller interior circle.
Peterson topped his previous single-season best of 1,760 yards in 2007 on a 52-yard run in the fourth quarter. On both long runs, Peterson made something out of nothing with nimble cutbacks to daylight.
Christian Ponder had a turnover-free game and ran for the game's first score for the Vikings, who had been just 1-5 on the road with the other victory at Detroit in September. Rookie kicker Blair Walsh was perfect on five field-goal attempts, three of them from 50 yards and beyond.
The Rams stopped Peterson, held to minus-3 yards on five carries, but not Ponder on the Vikings' opening drive. Benefiting from a short field at the St. Louis 45, the quarterback was 3 for 3 for 38 yards plus a 5-yard scramble that put them up 7-0.
Rookie Brian Quick won a jump ball with A.J. Jefferson in the end zone on a 4-yard reception, landing just inbounds to tie it early in the second quarter.
Then, the Vikings took over.
Peterson's 82-yard score came on the next play, Walsh's 50-yard field goal made the Rams pay for Bradford's botched snap and Griffen's interception return gave Minnesota 17 points in a span of just 3:56.
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Minnesota 36, St. Louis 22
Minnesota 7 23 3 3 36
St. Louis 0 7 0 15 22
Min • Ponder 5 run (Walsh kick), 7:07.
StL • Quick 4 pass from Bradford (Zuerlein kick), 12:39.
Min • Peterson 82 run (Walsh kick), 12:21.
Min • FG Walsh 50, 9:11.
Min • Griffen 29 interception return (Walsh kick), 8:25.
Min • FG Walsh 38, 3:11.
Min • FG Walsh 42, :00.
Min • FG Walsh 53, 5:56.
StL • Amendola 6 pass from Bradford (Zuerlein kick), 13:39.
StL • Kendricks 6 pass from Bradford (Amendola pass from Bradford), 7:48.
Min • FG Walsh 51, 5:31.
Attendance • 55,751.
First downs 18 29
Total Net Yards 322 432
Rushes-yards 33-213 18-87
Passing 109 345
Punt Returns 1-15 3-16
Kickoff Returns 1-24 2-29
Interceptions Ret. 1-29 0-0
Comp-Att-Int 17-24-0 35-55-1
Sacked-Yards Lost 2-22 4-32
Punts 4-45.5 4-41.0
Fumbles-Lost 2-0 2-1
Penalties-yards 3-49 8-47
Time of Possession 30:27 29:33
Rushing • Minnesota, Peterson 24-212, Ponder 4-6, Gerhart 5-(minus 5). St. Louis, Jackson 13-73, Bradford 2-9, D.Richardson 3-5.
Passing • Minnesota, Ponder 17-24-0-131. St. Louis, Bradford 35-55-1-377.
Receiving • Minnesota, Simpson 4-27, S.Burton 3-22, Rudolph 3-22, Carlson 3-17, Gerhart 2-21, Jenkins 1-11, Wright 1-11. St. Louis, Jackson 8-73, Gibson 6-76, Amendola 6-58, Pettis 5-55, Kendricks 3-35, D.Richardson 3-25, Quick 2-12, Givens 1-22, Harkey 1-21.
Missed Field Goals • St. Louis, Zuerlein 57 (WR).