The Saints (6-8) moved into first place ahead of Carolina (5-8-1) and Atlanta (5-9) and came away with the win after dropping four of five. They also rebounded from a 41-10 loss to the Panthers.
Brees, shaky last week, was spectacular this time.
He completed 29 of 36 passes and reached the 4,000-yard mark for the ninth straight year. He threw two touchdown passes to Josh Hill and another to Marques Colston.
Pierre Thomas had five catches for 83 yards. David Hawthorne had three of New Orleans' seven sacks and the Saints intercepted three of Jay Cutler's passes to bring his NFL-leading turnover total to 24.
The Bears dropped to 5-9.
