ATLANTA -- The defending NFC South champion Atlanta Falcons showed Thursday night that they aren't ready to concede the division title just yet.
Matt Bryant provided the winning margin on a 52-yard field goal with just under four minutes as the Falcons (8-5) moved within a game of the Saints (9-4).
After Jones' interception, the Falcons were able to run out the clock with the help of an unsportsmanlike-conduct penalty on Saints coach Sean Payton.
The Falcons won despite three interceptions by Matt Ryan, who finished 15 of 27 for 221 yards and a touchdown.
Brees completed 26 of 35 passes for 271 yards and two touchdowns but threw the costly interception.
Brees had to carry more of the load for the Saints after versatile rookie running back Alvin Kamara sustained a concussion on the game's first series.
The Falcons forced a tie with just under 10 minutes left on an 8-yard pass from Ryan to Mohamed Sanu. The play capped an 11-play, 69-yard drive that took more than seven minutes.
Ryan, who was picked off by Marshon Lattimore at the end of the first half, had his first pass off the second half intercepted by Chris Banjo. The Saints cashed the turnover in on a 1-yard scoring pass from Brees to Michael Thomas for a 17-10 lead.
The first half ended in a 10-10 tie when a 47-yard field goal by Wil Lutz was nullified by an illegal formation and the Saints didn't get another play with time expired.
Earlier jn the second quarter, the Falcons consumed more than eight minutes in going 90 yards in 15 plays, with Devonta Freeman scoring from the 1-yard line, to go ahead.
The Saints answered quickly, though, as Brees connected with Tommylee Lewis for a 26-yard touchdown.
The Saints lost Kamara on the game's opening drive, which ended with a 34-yard field goal by Lutz that was matched by a 28-yard field goal by Bryant.
Kamara, who came in with 1,220 yards from scrimmage and 11 touchdowns, was hurt on a helmet-to-helmet hit by linebacker De'Vondre Campbell while being dropped for a 4-yard loss on a pass from Brees.
Kamara, a third-round draft pick from Tennessee who grew up outside Atlanta, had three catches for 25 yards and one rush for 2 yards before being hurt.
NOTES: The Saints lost LB A.J. Klein (groin) in the first quarter, and S Kenny Vaccaro (groin) and DE Trey Hendrickson (ankle) in the second quarter. ... CB Desmond Trufant (concussion) and NB Brian Poole (lower) returned for the Falcons after missing a game. ... Saints rookie CB Marshon Lattimore had an interception in his return after missing two games with an ankle injury. ... FS Marcus Williams (groin) also returned for the Saints. ... Falcons LG Andy Levitre (triceps) had his streak of 140 consecutive starts broken. It had been the longest active streak for an interior lineman in the NFL. ... The Saints were without LG Andrus Peat (groin) and his replacement, G/C Senio Kelemente, sustained a concussion in the second quarter. ... Former RB Warrick Dunn became the 10th member of the Falcons' Ring of Fame during halftime ceremonies. ... The Saints and Falcons play in New Orleans on Dec. 24.