Roman Harper secured the win when he intercepted a tipped fourth-down pass in the end zone with under a minute left.
Brees connected with Marques Colston for a 25-yard touchdown pass during which the receiver also set a franchise mark for catches with 533. Brees also hit tight end Jimmy Graham for a 7-yard score in the third quarter.
Matt Ryan passed for 304 yards and touchdown passes to Tony Gonzalez and Julio Jones. He also drove Atlanta to the Saints 3 in the final minute before falling just short.
CHIEFS 28, JAGUARS 2
JACKSONVILLE, Fla. (AP) — Alex Smith threw two early touchdown passes, Kansas City's defense dominated all day and the Chiefs began the Andy Reid era with a victory at Jacksonville.
Jamaal Charles ran for 77 yards and a touchdown before leaving the game with a quadriceps injury, but that was about the only negative for the Chiefs.
Jacksonville advanced past its own 36-yard line just once, a stunning display of offensive futility for the rebuilding franchise. The Jaguars finished with 178 yards, but for most of the game were challenging the team low of 117 yards set last year against Houston.
It wasn't even close to the start the new coach Gus Bradley wanted, but it was a clear indication of how far the team has to go.
BEARS 24, BENGALS 21
CHICAGO (AP) — Jay Cutler passed to Brandon Marshall for the go-ahead touchdown in the fourth quarter, helping Chicago get the victory in Marc Trestman's coaching debut with the team.
It wasn't quite the display the Bears were looking for after making some big changes in the offseason. But it was good enough.
The Bengals led by 11 in the third quarter and were up 21-17 early in the fourth when Tim Jennings jarred the ball from Mohamed Sanu following a reception and made the recovery.