Winger John Rudd's early try put the visitors on the front foot and three penalty goals from New Zealand fullback Bruce Reihana helped the Saints to a 14-7 lead at halftime, despite the loss of England hooker Steve Thompson to the sin-bin.
Reihana banged over a fourth penalty goal from long range to settle his side's nerves in the 48th minute and things looked good for the English club when Narbonne's inspirational back-rower Christian Labit was sent to the sin-bin.
England winger Ben Cohen scored in the corner after some good work from Jon Clarke, and Labit's second yellow card and one to former Test prop and Narbonne try-scorer Franck Tournaire ensured Saints returned home with the points.
With Bristol expected to despatch Italian minnows Viadana on Sunday, Pool One should be decided on January 14 when Saints host their English rivals at Franklin Gardens.
In Pool Three, Bayonne bagged a predictable 45-6 victory over Romanian club Bucuresti but must beat Gloucester at Kingsholm in the final round to have any chance of topping the group.
Winger Vincent Noutary and hooker Christophe Laurent both scored try doubles in the one-sided match.