The Falcons (10-6) claimed the second wild-card berth in the NFC with the victory, while the Panthers (11-5) had to settle for the first wild-card spot rather than the NFC South title because of the loss. Carolina finished in a tie with New Orleans, which lost 31-24 at Tampa Bay, but the Saints beat the Panthers twice during the season to earn the division title and home field in the first round.
The Saints and Panthers will meet in New Orleans next Sunday at 4:40 p.m. ET in the opening round of the playoffs.
Bryant's fifth field goal, from 33 yards with 2:27 remaining, came after Newton threw his second of three interceptions, this one by safety Keanu Neal.
Newton misfired on his first nine passes and finished 14 of 34 for 180 yards and one touchdown while being sacked twice. His third interception by cornerback Robert Alford, came in the end zone on the next-to-last play of the game.
Falcons quarterback Matt Ryan was 28 of 45 for 318 yards and a score.
The Falcons, NFC champions a year ago, went ahead in the third quarter on field goals of 30 and 42 yards by Bryant, then led by nine points after his 30-yarder in the first minute of the fourth quarter.
Bryant's first field goal came after video review overturned an apparent 12-yard touchdown pass from Ryan to Mohamed Sanu, and the second followed an interception by safety Ricardo Allen. His third field goal capped a drive of 60 yards.
A 44-yard field goal by Graham Gano got the Panthers back within six points, but Bryant connected on his 56-yarder with 6:37 remaining to make it a two-score game.
Neal's interception to set up Bryant's final field goal came on a high pass that went off the hand of Panthers tight end Greg Olsen.
The Panthers drove 78 yards in 16 plays, holding the ball for more than eight minutes, to tie the game 7-7 on a 4-yard touchdown pass from Newton to Devin Funchess with 50 seconds left before halftime.
Newton was 7 of 7 for 66 yards on that drive after going 0 of 9 on the Panthers' first four possessions.
The Falcons scored on their first possession for just the fourth time this season as running back Devonta Freeman covered 19 yards with a short pass from Ryan to cap a 10-play, 75-yard drive after the opening kickoff.
NOTES: The Panthers were without three starters -- RB Jonathan Stewart (back tightness), RG Trai Turner (concussion) and FS Kurt Coleman (ankle). Turner was ruled out of his third straight game Friday, while Coleman had been listed as questionable. Stewart was not on the injury report. ... Falcons C Alex Mack (calf) started, but LG Andy Levitre, who had missed the previous three games, reinjured his triceps on the game's first series. ... Falcons WR Taylor Gabriel (hamstring) left the game in the first quarter and DE Adrian Clayborn limped off in the fourth quarter. ... TE Levine Toilolo (knee) was inactive for the Falcons. ... DT Vernon Butler (shoulder) left the game in the second quarter for the Panthers and TE Chris Manhertz (ankle) was lost in the third quarter.