But as the two teams head toward Sunday's matchup at the Edward Jones Dome, the circumstances of this meeting aren't much different than the last time they met.
That was in 2011, a game in which the 0-6 Rams stunned the 5-2 Saints in surprisingly convincing fashion 31-21 at the Edward Jones Dome. It was a Rams team already essentially out of the race with a backup quarterback taking on a powerful Saints team firmly in the playoff picture.
For the Saints players still with the organization, that memory has them on full alert for the dreaded trap game that could await them in St. Louis. It's a fear heightened by the fact that this meeting comes squarely between two huge NFC South games against second-place Carolina.
"They all concern me," New Orleans quarterback Drew Brees said. "They all give me stress. Despite what their record might show, there's just a level of pride and we also know the times where we've gone there and played in '09 and '11 and they've been tough, hard-fought games. Last time we went, we got whooped, no bones about it. And we all remember that, the guys that were here, and we know it's going to take a much better performance on our part this time around in order to get a win."
On the other side of the ledger, it's much easier to spring a trap if you haven't already used it on the same target. More relevant, it's going to take a much better performance than what the Rams have provided the past two weeks to pull of a surprise repeat of 2011.
Rams linebacker Jo-Lonn Dunbar was on the other side of the matchup and has vivid memories of what happened that day. For those who might have forgotten, the St. Louis Cardinals baseball team had just won the World Series and was honored at the game.
Many of the Cardinals were in attendance and brought the World Series trophy along with them. The mere presence of the Cardinals energized the Edward Jones Dome crowd and, by extension, the Rams.
The Rams' defense, in particular, put together the blueprint on how to harass Brees, getting to him six times for sacks and spending most of the day in his face. End Chris Long had three of those takedowns and even played to the baseball theme by "hitting a home run" as his sack celebration.
"I just remember their defense making big play after big play and we couldn't get them off the field on third downs," Dunbar said. "I think the Cardinals had won the World Series that year and everybody was pretty loud in there, especially when those guys [the Cardinals] came in. We didn't play well and they definitely got after us."
The Rams went on to a dreadful 2-14 season and that game remained as essentially the only highlight in a season of lowlights. The Saints would go on to a 13-3 finish.
Since, as is always the case in the NFL from year to year, much has changed on both sides. The Rams have gone under a major reconstruction under new coach Jeff Fisher and staff and the Saints have gone through a trying season caused by the suspension of head coach Sean Payton.
As they reconvene Sunday, not much remains from that meeting.
"I think this is a much different team -- well, both teams are, obviously," Payton said. "I think they're a much better team that we're seeing this week than the one we saw in '11 and yet it's the nature of our game, when you turn the football over and you don't protect the quarterback and you have a punt blocked, shoot, that game wasn't really even close in '11. There are a lot of new faces and the rosters are much different."
Past success guarantees nothing in the NFL but there is something instructive from that game that both teams can take away. From the Saints, the lesson is simple, anything can happen in any week, regardless of record or pedigree.
"I'm sure they're aware of it," Dunbar said. "I'm sure it's something Sean has pointed out numerous times so they're going to be ready to play us."
For the Rams, it's the same lesson only from the other angle. For whatever reason, the Rams have consistently played the Saints close in recent meetings. Dating to 2004, the Rams and Saints are tied 3-3 in six meetings and the Rams have outscored them by a grand total of three points in those meetings.
Even in 2007, a 0-8 Rams team went to New Orleans and got its first win of the year against the Saints.
On paper, this once again looks like a bad matchup for the Rams, particularly without starting quarterback Sam Bradford and with a struggling young secondary forced to take on the Saints' high-powered offense.
For all intents and purposes, it's a game that probably shouldn't be close but that's a message the Rams don't want to hear. Their focus isn't on past upsets so much as finding a way to finish another lost season with a flourish.
"I think the guys from this locker room understand that we are trying to end this season with the arrow going up," middle linebacker James Laurinaitis said. "I think we'd all lie to you if we said this wasn't a disappointing season but we want the arrow pointing up at the end of the year and we want to end on a positive note. If you can't get up to play the New Orleans Saints ... then something is not right in your DNA."