That would be the 1940 Chicago Bears.
Atlanta coach Jim Mora Jr. said he doesn't care which foe his team faces. "I'm just happy that we are playing," he said.
The Rams were looking for all the comforts of home when they brought their "Greatest Show on Turf" to the cozy environs of the Georgia Dome.
But Michael Vick and the Falcons (12-5) taught the Rams (9-9) indoor relative humility. Vick completed 12 of 16 passes for 82 yards and two touchdowns. More impressively, he rushed eight times for 119 yards.
"This is a very exciting time for us," Vick said. "The whole world is watching. This is something we've worked for all year. Why not go out there and enjoy the moment?"
Warrick Dunn ran for 142 yards on 17 carries and two touchdowns.
"We ran the ball pretty well tonight," Mora said. "I think that's a credit to our entire offensive team.
"You saw a team that plays together. You saw a team that's pretty complete. We like to say in the locker room that the best player on our team is our team. We proved that tonight with the way we played."
Atlanta's Allen Rossum established an NFL postseason record with 152 yards on three punt returns.
"I truly left it all out on the field," Rossum said. "I'll have no trouble going to sleep tonight."
The Falcons earned their first-round bye and a home playoff game by winning the NFC South.
Vick, the league's preeminent all-purpose quarterback, wasted little time asserting himself, scrambling, then sprinting 47 yards to the Rams' 21-yard line during the Falcons' opening drive.
Two plays later, Vick fired a dart to tight end Alge Crumpler for an 18-yard touchdown strike. The extra point by Jay Feely made it 7-0 just three minutes into the the game.
Vick said St. Louis tried a new defensive strategy last night. "But it backfired," he said.
The Rams, who were operating without the services of injured wide receiver Isaac Bruce, answered immediately with a 5-play, 81-yard drive, capped with a 57-yard pass from Marc Bulger to Kevin Curtis to tie the score 7-7.
Atlanta defensive linemen Patrick Kerney, Rod Coleman, Brady Smith and Ed Jasper had a league-high 48 sacks during the season. But Bulger managed to complete 11 of 17 first-half passes for 190 yards and two touchdowns. Coleman finally reached Bulger for a sack midway through the third quarter.
Atlanta used another big play to regain the lead, 14-7. This time it was Dunn bursting through the line and out-sprinting the Rams secondary for a 62-yard TD.
Dunn gave the Falcons a 21-7 advantage with his second TD of the game, this one from 19 yards out to culminate a 13-play, 80-yard march early in the second period.
Bulger passed 28 yards to Torry Holt in the deep corner of the end zone to pull St. Louis within 21-14. But Atlanta once again was revived by a 68-yard punt return for a touchdown by Rossum with 59 seconds left in the first half.
"Give them credit," Bulger said. "They are a good team. Their coaching staff had them ready to go."
The Rams' Curtis led all receivers with seven catches for 128 yards and a score.
"I would trade it all for a win," Curtis said.
The Chicago Tribune is a Tribune Publishing newspaper. The Associated Press contributed to this article.