Jackson carried the ball 25 times, scoring on a 3-yard runs in each of the second and third quarters for the Rams, who logged their first win after opening the season with six consecutive losses.
Backup quarterback A.J. Feeley filled in for in the injured Sam Bradford for a second straight week and responded by going 20-of-37 through the air for 175 yards and an 8-yard touchdown pass to Brandon Lloyd.
Drew Brees was picked off twice for the Saints (5-3), finishing 30-of-44 for 269 yards and a touchdown.
Lance Moore made eight grabs for 82 yards and a score in New Orleans' loss.