ATLANTA -- Matt Ryan's late-game quarterback magic, missing the past two games in narrow losses by the Atlanta Falcons, resurfaced Sunday.

Ryan hit wide receiver Mohamed Sanu in the end zone for an 11-yard touchdown with 31 seconds remaining, and Matt Bryant's extra point gave the Falcons a 33-32 victory over the Green Bay Packers.

"They don't call him 'Matt Ice' for nothing," said Sanu, who left Cincinnati to sign as a free agent with the Falcons during the winter. "He has ice in his veins."

The nickname was in question, though, after late interceptions the previous two weeks against Seattle and San Diego had proven costly.

This time the Falcons drove 75 yards in 11 plays for the victory after the Packers went ahead with just under four minutes left on a 7-yard touchdown pass from Aaron Rodgers to Jeff Janis and Rodgers' two-point conversion run.

"It was one of those back-and-forth games and this time we finished," said Sanu, who had nine catches. "The last two games, we didn't."

Ryan, going over 200 yards for a NFL-record 47th consecutive game, completed 28 of 35 passes for 288 yards and three touchdowns as the Falcons (5-3) ended a four-game, head-to-head losing streak to the Packers (4-3).

"We had a match-up we liked on the linebacker and (Sanu) stayed patient on the rout," Ryan said of the winning throw. "He's a big body who is excellent in the red zone. I saw an opportunity to give him a high ball and he came down with his feet in."

Rodgers was 28 of 38 for 246 yards and four touchdowns, and he also ran for a team-best 60 yards on six scrambles. He couldn't get the Packers within range for a field-goal attempt in the final seconds, though.

"We needed a win like this," said Falcons defensive end Adrian Clayborn, who had two of the Falcons' three sacks. "We didn't need a blowout. We needed a game like this to show that we could win it."

It was a game of long drives, the Packers going 86 yards on 13 plays in the fourth quarter to take the lead after the Falcons went 80 yards in 14 plays to go up 26-24 in the third quarter, that march climaxed by Devonta Freeman's 1-yard touchdown run.

The Packers were shorthanded on offense and defense because of injuries, but almost pulled out a victory anyway.

"First, there are no excuses," Rodgers said. "I'm proud of our guys. I'm proud of the way everyone battled. This is an important time for us to stick together and figure out what we have to do to go on a run."

"I'd like to get back to the no huddle, we have a quarterback who is exceptional at it," said coach Mike McCarthy, who at the moment doesn't have the healthy personnel to use it. "We're playing everyone we have."

The Packers led 24-19 at intermission. Rodgers completed 17 of 21 passes for 170 yards and three touchdowns before the break. He also scrambled 23 yards to spark a quick-strike drive that resulted in Mason Crosby's 29-yard field goal on the last play of the half.

The Falcons failed on a two-point attempt after Ryan's 5-yard touchdown pass to Freeman with 27 seconds remaining in the second quarter, but they left enough time for the Packers to add to their lead.

Rodgers' first-half touchdown passes covered 5 yards to Jordy Nelson, 4 yards to Geronimo Allison and 9 yards to Trevor Davis, who set up the score with a 55-yard punt return.

Ryan was 16 of 20 for 183 yards and two touchdowns in the first half, with the Falcons' opening score coming on a 47-yard bomb to Taylor Gabriel.

Bryant kicked field goals of 36 and 40 yards in the first half, breaking the Falcons record of 806 career points set by Morten Andersen during his two stints with the team.

NOTES: The Falcons lost TE Jacob Tamme to a shoulder injury on their opening possession. He was hurt when tackled after a 13-yard reception, his second catch. ... The Packers were without LB Clay Matthews (hamstring), WR Randall Cobb (hamstring) and WR/RB Ty Montgomery (illness). All had been listed as questionable on the injury report. ... CBs Quinten Rollins (groin) and Damarious Randall (groin), RB James Starks (knee) and TE Jared Cook (ankle) were previously declared out by the Packers. ... The Falcons were without RB Tevin Coleman (hamstring). ... Non-injury inactives for the Falcons included CB Jalen Collins and DT Ra'Shede Hageman, both former second-round draft picks. ... It was the first of four road games in five weeks for the Packers, who were coming off four straight home games. ... The Packers were the second straight Falcons opponent to have 10 days off before the game. ... The Falcons have a short week coming up, as they play at Tampa Bay on Thursday.