The Ravens were led by running back Kenyan Drake, who rushed for 93 yards and two touchdowns, while quarterback Lamar Jackson added a touchdown and 82 rushing yards of his own.
The momentum was all with the visitors early, as Baltimore found the end zone twice in the first half while restricting the Saints to a lone field goal.
Both offences stalled after the break with each team only managing a field goal to make for a 17-6 score line headed into the fourth quarter.
Any hope New Orleans had of pulling off a late comeback was then quickly put to bed when a Justin Tucker field goal was followed by Drake's second touchdown of the day.
A late touchdown pass to Juwan Johnson was the only highlight of the game for Saints quarterback Andy Dalton, who also threw an interception in the 14-point defeat.