Brees connected on an 8-yard score to Lance Moore with 2:37 remaining to give New Orleans (5-3) the win in a game waged between the past two Super Bowl winners.
Brees finished the night 34-of-44 passing for 305 yards, with two touchdowns and an interception. Seven of those completions were collected by Moore, who gained 54 yards with a touchdown.
Marques Colston grabbed six passes for 75 yards and a score on a night when the Saints were playing without running backs Reggie Bush and Pierre Thomas.
Steelers signal-caller Ben Roethlisberger completed 17-of-28 passes for 195 yards and an interception.
Rashard Mendenhall racked up 71 yards on 15 carries for the Steelers (5-2).