In what may prove to be a costly victory because of injury, the Falcons defeated the St. Louis Rams 31-24 before an announced crowd of 70,056 fans Sunday at a raucous Georgia Dome.

“It was a good win for our team today,” Falcons quarterback Matt Ryan said. “You like to get that first one as fast as possible. It was nice to get it today.”

The Falcons came out and jumped on the not-ready-for-prime time Rams and then held on, with five starters out, as massive injuries mounted.

Fullback Bradie Ewing (shoulder), running back Steven Jackson (thigh), defensive end Cliff Matthews (neck), cornerback Asante Samuel (thigh), linebacker Kroy Biermann (ankle) and linebacker Sean Weatherspoon (foot) all left the game in the first half.

Matthews, a special teamer, was the only player from the group who returned to the game.

“I thought that was a hard-fought football game between too physical football teams,” Falcons coach Mike Smith said. “We were able to prevail. We were able to make enough plays to get the win.”

Under Smith the Falcons now have a 21-3 record (.875) after regular-season losses.

Shortly after losing to the opener to New Orleans last Sunday, Smith was already embedding the notion into his team’s psyche. Several players were robotically reciting the corny “streak stops at one” mantra after that loss.

The last time the Falcons dropped back-to-back regular-season games was in 2009 against the Eagles (34-7) on Dec. 6 and the Saints (26-19) on Dec. 13.

The Falcons have now won after their last 13 losses and improved their record at the Georgia Dome to 34-7 under Smith.

The Falcons improved to 1-1 on the season, while the Rams dropped to 1-1.

Backup running back Jason Snelling, in the game for Jackson, plowed into the end zone from 11 yards out with 6:12 to play to help secure the victory.

Wide receiver Julio Jones was nearly unstoppable as he caught 11 passes for 182 yards and an 81-yard touchdown, the longest of his career. Roddy White again served mostly as a decoy as he caught three passes for 21 yards.

“It’s impressive, but I’m not surprised,” tight end Tony Gonzalez said. “Matt Ryan is one of the best in the business and so is Julio Jones. You are going to be hearing those two names for a long time around here. It’s a sign of good things to come.”

The Falcons opened the game with a long touchdown drive and then added two big plays for touchdowns as they jumped out to a 21-0 lead against the dazed St. Louis Rams.

After an exchange of field goals, the Falcons held a 24-3 lead at halftime.

The Falcons opened with an 11-play, 80-yard touchdown drive. Ryan, who was throwing the ball quickly, before the Rams’ pass rush could get to him, completed seven of eight passes for 75 yards during the drive.

After going 3 of 11 on third down last week, the Falcons converted on their first two third downs in the drive. Tight end Tony Gonzalez caught a pass on a third-and-7 from the Falcons’ 23 for an 11-yard gain and Harry Douglas broke free up the left seam for a 20-yard gain on a third-and-8 from the 50.

Three plays later, Ryan tossed a swing pass out to Jackson who scored from 8 yards out. White was in on the play as a decoy as Jackson ran into the space that White cleared out.

Jackson suffered a thigh injury on the play and did not return.

After the Rams stalled twice, the Falcons, on their third possession of the game, caught the Rams in an all-out blitz on third-and-7 from their 19. Ryan lofted a nice pass out to Jones at the Falcons’ 44-yard line. He’d gotten behind Rams cornerback Janoris Jenkins and won a 56-yard foot race to the end zone.

The Rams finally started to move the ball and were down to Atlanta’s 32-yard line. On first-and-10, Sam Bradford’s pass to running back Daryl Richardson skidded off his hands and into the arms of Falcons defensive end Osi Umenyiora, who ran 68 yards for a touchdown. Matt Bryant’s extra point made it 21-0.

“I didn’t want to drop the ball,” Umenyiora said. “That would have been the worst play of my career. So I just tried to hold onto it.”

Umenyiora had never played in a two-point stance in his NFL career until joining the Falcons.

“I would prefer to rush, but at the same time whatever they ask me to do, I will do,” Umenyiora said.

Rams kicker Greg Zuerlein made a 29 yard field goal and Bryant added a 38-yarder for the halftime margin.

The Falcons had blown double-digits leads of 20, 17 and 10 points in their last three outings. The Rams closed within seven, 24-17, after touchdown passes to Tavon Austin and Austin Pettis with under 12 minutes to play.

The Falcons answered with a nine-play, 80-yard drive that was capped by Snelling’s touchdown.

The Rams wouldn’t go away.

Bradford drove them down for another score. He tossed a 10-yard touchdown pass to Austion with 2:09 left to play to cap a 16-play, 80-yard drive.

The Falcons will swing into the heavy AFC East portion of their schedule with a road game at Miami before hosting New England on Sept. 29 and the New York Jets on Monday, Oct. 7