The Saints (6-8) are comfortably the worst division leaders in the eight groups, but are within touching distance of the post-season after a Drew Brees-inspired victory at Soldier Field in Illinois.
Brees drove the Saints 375 yards and completed 29 of 36 pass attempts, including three touchdown completions.
Opposite number Jay Cutler threw two final-quarter touchdown passes for the Bears, as he amassed 194 yards - but the scores were mere consolation for Chicago, who prop up the NFC North with a 5-9 record.
Brees, meanwhile, passed 4000 yards in a season for the ninth consecutive season, and delivered two TD receptions to Josh Hill, and another to Marques Colston.
A scoreless first quarter was epitomised by both sides losing possession in the opening seconds, before Brees found Hill for an eight-yard TD and Colston on a nine-yard play as the Saints led 14-0 at the break.
Hill got his second TD on a seven-yard pass from Brees in the third quarter, before a Shayne Graham field goal made it 24-0.
The Bears would get on the board in the final quarter, but it was too little, too late - New Orleans' win sealed when Mark Ingram, who rushed 59 yards in the match, produced a 15-yard TD run.