"When you looked at their sideline, they realized, `Oh gosh, like, here we go again,'" Rams defensive end Chris Long said. "We hit `em early, and they were reeling."
The Rams were 0-6 and double-digit underdogs before upsetting the Saints in 2011. St. Louis was 2-14 that year and New Orleans went 13-3.
Everything went sour fast for the 10-win Saints. Brees was intercepted on the first snap, and again in the second series, and the Saints played catch-up all day.
"You want to talk about waking the whole place up," Brees said. "That did it."
Quinn had two sacks, giving him an NFC-leading 15, for a pass rush that took the heat off a young secondary. His quarterback hit on the Saints' first snap of the game altered the flight of the ball on T.J. McDonald's interception, and he had a sack, strip and fumble recovery to keep the Saints down in the third quarter.
Coach Sean Payton benched left tackle Charlie Brown after that play and shifted left tackle Zack Strief to the right side in an attempt to neutralize Quinn.
"I saw enough. Period. I mean, enough," Payton said.
The Saints (10-4) missed their first chance to clinch a playoff berth, trailing 24-3 at the half, but made it look respectable with two touchdowns in the fourth quarter. They're unbeaten at home, but just 3-4 on the road and play at Carolina with the NFC South lead on the line next week.
The Saints are averaging 32.9 points at home, with five of the wins by double-digits including playoff hopefuls Dallas and Arizona. They're averaging just 18.4 points on the road with the three wins by eight, four and two points.
Kellen Clemens threw for two TDs in the first quarter, matching his best performance in seven games as the fill-in starter for Sam Bradford. The Rams (6-8) recovered an onside kick to set up a field goal in the first quarter, and Michael Brockers blocked a field-goal attempt at the end of the half.
Brees was 39 for 56 for 393 yards, but with just one touchdown, and threw two interceptions in the first quarter for the first time in a decade.
The Rams played one of their strongest games of the year a week after getting eliminated, and the franchise is assured of a 10th consecutive season without a winning record.
St. Louis' offense had a nice day against Saints defensive coordinator Rob Ryan, who had an extended interview with the Rams in January before joining New Orleans.
"When people change their mind, they change their mind, and I was fine with that," coach Jeff Fisher said. "He's a good coach."
Stacy shook off an early hip injury scare and set a franchise rookie record with 106 yards by halftime, bettering the likes of Hall of Famer Eric Dickerson, Steven Jackson and Jerome Bettis. Stacy finished with 132 yards on 27 carries.
"Questionable? Nah, I was never questionable," Stacy said. "I was always going back. I'm a competitor."
Brees scored on a 1-yard sneak and threw a 5-yard touchdown pass to Marques Colston with 3:07 to go. The Saints recovered an onside kick, but their comeback ended when Garrett Hartley was wide left on a 26-yard field-goal attempt.
Last week, Brees became the fastest in NFL history to 50,000 yards passing while throwing for four TDs in a 31-13 victory over Carolina at home.
Cory Harkey broke three tackles on a 31-yard touchdown catch the first play -- just his seventh reception of the year after Brees' first interception.
Brees floated a rollout aimed at Jimmy Graham, who was in triple-coverage, and Trumaine Johnson snared another underthrown pass at the goal line. The Rams drove 93 yards, helped by a pair of personal penalties, and made it 14-0 on Clemens' 4-yard pass to a wide-open Lance Kendricks.
The Rams followed up with perfect execution on an onside kick by kicker Greg Zuerlein recovered in the air by a leaping Stedman Bailey, setting up a field goal for a 17-0 cushion early in the second quarter.
Clemens got a chance to use the victory formation the Rams practice after Brockers blocked Hartley's 36-yard field-goal attempt with two seconds left.
Former Rams two-time Pro Bowl QB Marc Bulger, holding his daughter, was introduced during the break while Stacy was helped off the field. ... According to STATS, the first seven games, the Saints forced 15 turnovers and scored 48 points. They had no turnovers or sacks against the Rams, and over the last seven games they have just two takeaways.