"I think it says a lot about the maturity of the team," Bradford said. "I think this team grew up a little bit more today."
For Bradford, the 2010 No. 1 draft pick enjoyed his second consecutive fourth-quarter comeback victory after rallying the Rams to a 16-13 overtime win over San Francisco last weekend.
And this time it happened outside the comforts of their climate-controlled dome, and on an afternoon that featured temperatures in the high 30s, and a drizzle that fell through much of the second half.
The Rams (6-6-1) stayed in the playoff hunt by winning three in a row for the first time since 2006. They improved to 2-6 outside the NFC West by winning for only the second time on the road this season.
"I think a lot of the guys this year have more confidence and they're more determined," tight end Lance Kendricks said. "They want it. They want it more than the other team."
Bradford finished 19 of 39 for 209 yards and an interception. Steven Jackson had 64 yards rushing and scored on a 1-yard plunge, while Gibson made six catches for 100 yards.
Bradford delivered in the clutch by converting a pair of third-down attempts, including a third-and-10 by threading a 15-yard pass to Gibson, and a fourth-and-1.
On the touchdown, Bradford rifled a pass over the middle that a leaping Gibson caught just a step ahead of rookie cornerback Ron Brooks.
"Sam's not a guy who gets flustered," coach Jeff Fisher said.
The Bills (5-8) did.
Their defense squandered a lead in the final 2 minutes at home for the second time this season after unraveling in familiar fashion in a 35-34 loss to Tennessee on Oct. 21.
Safety George Wilson twice had chances to intercept Bradford on the final drive, only to drop the ball each time.
"You have to be a finisher in this league," Wilson said. "Those are the plays you replay over and over in your head, wishing that the ball would've bounced your way."
If it's any consolation, there was plenty of blame to be laid on an offense that lacked finish.
Buffalo came away with two field goals on three drives inside the Rams 25. That included Fred Jackson losing a fumble at the Rams 14.
"Bottom line, we could not make plays to win the ballgame," coach Chan Gailey said. "It is a bitter pill to swallow."
The injury count continues to mount. Already down starting center Eric Wood (left knee) and right guard Chris Hairston (right ankle), Jackson had to be helped off the field after appearing to hurt his right leg with about 5 minutes left.
Jackson's leg was sandwiched by two Rams as they made a tackle on a 2-yard run near midfield. With a towel over his head, Jackson was then carted off from the sideline, with fans chanting "Freddie! Freddie!"
Jackson is out a minimum of two to three weeks according to Gailey, which means his season probably is over.
Fitzpatrick went 25 of 33 for 247 yards passing, including a 2-yard touchdown to Lee Smith.
"We've got to develop a killer instinct," Fitzpatrick said. "And we've got to win these games if we want to be one of the teams that's sitting there at the end of the year ready for the playoffs."
Rather than gaining ground on Cincinnati and Pittsburgh (they both lost Sunday, and fell to 7-6) in the AFC playoff race, the Bills are all but mathematically out of the hunt. That's a familiar position for a team that's not been to the postseason since 1999, the NFL's longest active drought.
Things are looking brighter for the Rams, a team that's not been to the playoffs since 2004 and has not won eight games since 2006.
Much of the credit for their resurgence comes as a result of a sturdy and aggressive defense. St. Louis limited the Bills to 281 yards and forced two turnovers. Rookie tackle Michael Brockers had 1 1/2 of St. Louis' five sacks.
"We're a motivated team," Brockers said. "The plane-ride home is going to be very enjoyable. We had a lot that weren't this year, but this one is going to be a good one."
Rams S Craig Dahl did not return after sustaining a concussion. LT Rodger Saffold couldn't finish because of a nagging back injury. ... The Bills allowed 78 yards rushing, extending their streak to four games of holding opponents under 90. That's the team's best stretch since a four-game streak in 1999. ... The Bills failed on an extra point when holder Shawn Powell had the ball slip through his hands. ... Bradford also completed a 2-point conversion with a pass to Chris Givens.
Information from The Associated Press and ESPN NFL Insider Adam Schefter was used in this report.