The Saints (6-1) were a little rusty coming off their bye week but the offense kicked it into gear during the middle two quarters as the Saints outscored the Bills 21-10 in that crucial two-quarter span.
Brees was 26 of 34 for 332 yards and the five touchdowns, a season high.
Graham, who was questionable all week with a foot injury he suffered two weeks ago against the Patriots, caught three passes for 37 yards, including 15-yard and a 13-yard TD receptions.
It was Brees' 22nd career game of four-plus TDs passing. Only Peyton Manning (25) and Brett Favre (23) have more in NFL history. It was the eighth time in Brees' career that he has thrown for five touchdowns, the most in NFL history. Brees topped the 200-yard mark for the 38th straight time.
"It was good to get the win," Coach Sean Payton said, "but there are things we have to get cleaned up."
The Saints' defense set the tone for the day when linebacker
The Bills, who dropped to 3-5 after the loss, played tough before the Superdome crowd of 72,405 fans. Lewis, despite taking numerous hits, was able to move the Bills at times and put some points on the board. He finished 22 for 39 for 234 yards and one touchdown with one interception. Veteran Fred Jackson was the top rusher for the Bills with 45 yards on 15 carries and a touchdown.
Payton said he played Graham after witnesses a pre-game workout from the big tight end, who was coming back from a foot injury. "Can he function, can he move, can get out of a cut," Payton said. "It worked well, I thought he handled it well."
The Saints play at the New York Jets next Sunday afternoon.