Atlanta held the ball almost twice as long as Arizona, stopped each of the Cardinals' eight third-down plays and intercepted three passes.
It was just the well-rounded performance the Falcons needed after a tough opening loss at Pittsburgh.
"We're going to be a more confident football team going into next week against New Orleans," said receiver Roddy White, who had seven catches for 78 yards and a touchdown.
The Falcons needed the momentum boost after opening the season with a 15-9 overtime loss at Pittsburgh.
"We had a little bit of a chip on our shoulder," said receiver Brian Finneran. "We felt like we let one slip away against a good football team up in Pittsburgh. So we needed to come down here and prove to ourselves and the rest of the league that we're still someone to be contended with."
"It's got to give us confidence but at the same time we're going against the world champions, so we know our plates are full," said tight end Tony Gonzalez. "We know we've got to duplicate what we did this week and maybe even keep rising up. We've got to get better.
"We're going to be a pretty good football team. We've got the talent. We just have to keep putting it together week in and week out."
Turner suffered a groin injury and was held out in the second half even after being cleared to return. He had nine carries for 75 yards before leaving the game in the second quarter.
Norwood was carted off the field with a knee injury. Coach Mike Smith said Monday he will say more on Wednesday about the severity of the injury.
"I know everybody's concerned about Jerious," Smith said. "Jerious has had some evaluation this morning and we're going to continue to evaluate it. Hopefully we'll have a lot more information on Wednesday."
Running back Antone Smith, who was not on the active list against Arizona, might be needed behind Turner and Snelling against the Saints.
The Falcons had 221 yards rushing, including 64 yards in the final quarter. Atlanta limited Arizona to 29 total yards in the final 15 minutes.
"We want to be able to run the football and possess the ability to finish games," coach Mike Smith said. "I thought it was evident that we did that. I thought that we were the tempo-setters in the game, and I think that's very, very important for any successful team."
The workhorse was Snelling, who averaged 5.4 yards on his 24 carries.
"Just says a lot about the depth of this team that our personnel staff has put together over three years," Smith said. He's just a darned good football player, not only running the football, but catching the football."
"We didn't have next week in mind," Ryan said. "I think the biggest thing was to focus on getting a win, and we were able to accomplish that."
Copyright 2010 by The Associated Press