Brees found five different receivers for each of his scores, which helps his own side towards reaching the post-season as the battle for the NFC South continues.
The Steelers, who are now 7-5, lose ground on the Cincinnati Bengals following their slim victory over the Tampa Bay Buccaneers earlier this evening.
Both offenses struggled to get going early on, with a pair of Shaun Suisham field goals for the Steelers the only points on the scoreboard midway through the second quarter.
With the first half coming to a close, Brees extended the Saints' advantage, targeting full-back Erik Lorig for a short score.
Brees had other ideas, however, targeting Kenny Stills downfield. The receiver collected the ball and travelled 69 yards to re-establish their two-score lead.
After a 47-yard Suisham field goal to kick off the final quarter, Marques Colston became the Saints' fifth scoring receiver of the day, making it a 19-point game heading into the last 10 minutes.
The Steelers refused to give up despite time ticking down, and Antonio Brown registered a score just before the two-minute warning. Roethlisberger then found the same man for a two-point conversion, keeping their hopes alive.
In the final seconds of the match, Roethlisberger and Brown connected again, with Lance Moore this time adding two.
However, it was too little, too late, allowing Brees and the Saints to improve their standing in the weakest division in the league.