Bijan Robinson was at the heart of Atlanta's victory, rushing for 145 yards and two touchdowns as the Falcons controlled the game from the opening possession.
Robinson sets the tone early
Atlanta needed only three offensive plays to make its mark.
Robinson broke through the Saints' defensive line and raced 59 yards for a touchdown, immediately silencing a packed Superdome that had gathered for celebrations marking the 20th anniversary of the stadium's reopening following Hurricane Katrina.
The Falcons continued to exploit New Orleans on the ground, with Robinson later adding a four-yard touchdown run.
Brian Robinson Jr. also enjoyed an outstanding night, rushing for 62 yards and three touchdowns as Atlanta's two Robinsons combined for five rushing scores.
Falcons take control before half-time
Atlanta established a commanding 24-7 lead by half-time.
Quarterback Michael Penix Jr., making his second consecutive start, completed 15 of 20 passes for 223 yards and one touchdown.
His most important scoring throw came in the fourth quarter when he connected with Jahan Dotson for a 31-yard touchdown, extending Atlanta's advantage and effectively ending any hopes of a Saints comeback.
The Falcons finished with 207 rushing yards compared with just 50 for New Orleans, highlighting their dominance at the line of scrimmage.
Saints struggle to keep pace
New Orleans managed to produce some moments of resistance, with Alvin Kamara scoring two rushing touchdowns.
Quarterback Tyler Shough completed 30 of 48 passes for 286 yards and a late touchdown pass to Devaughn Vele, but the Saints could not overcome the early deficit.
Chris Olave was another bright spot for the home side, recording eight catches for 116 yards.
However, New Orleans dropped to 1-3 after suffering its second consecutive defeat.
Emotional night ends in disappointment
The game carried considerable significance for New Orleans as the Saints celebrated two decades since their famous return to the Superdome after Hurricane Katrina.
Former Saints stars including Drew Brees, Scott Fujita, Scott Shanle and Deuce McAllister joined Steve Gleason for pre-match festivities, while Irma Thomas performed the national anthem.
The occasion ultimately belonged to Atlanta, however, as the Falcons spoiled the celebrations with their third consecutive victory over the Saints.
Falcons move into NFC South contention
The victory lifted Atlanta to 2-2, level with the Carolina Panthers at the top of the NFC South.
The Falcons have now won their last two games convincingly, including a 35-14 victory over the Green Bay Packers in their previous outing.
The return of Penix has coincided with Atlanta's improved form, with the quarterback now 2-0 as a starter this season.
Match summary
• Atlanta Falcons: 45
• New Orleans Saints: 24
• Venue: Caesars Superdome, New Orleans
• Competition: NFL, Week 4
• Standout: Bijan Robinson — 145 rushing yards, 2 touchdowns
• Falcons rushing: 207 yards
• Saints rushing: 50 yards