Robson had the luxury of being able to rest the likes of Alan Shearer, Shay Given and Gary Speed, as his side sat on a 5-0 lead from the first leg.
NAC rarely threatened an upset, despite Ton Lokhoff's side playing with real spirit, as Given's understudy Steve Harper kept a clean sheet and Laurent Robert pinched the win with a strike in the last five minutes.
Robson will be pleased to have grabbed a win, but the clean sheet will almost certainly raise morale at St James' Park.
NAC tried to fire their fans as Johan Elmander went close with a cheeky lob in the opening minute, while Orlando Engelaar's free kick fizzed narrowly wide.
Shola Ameobi stung Gabor Babos' palms with a low shot, but shortly afterwards NAC's plans were thrown into disarray as their keeper had to go off after colliding with Titus Bramble.
NAC almost pinched the lead when Marcel Koning's header beat Harper but agonisingly cannoned to safety off the woodwork.
The Dutch side ran out of ideas as the game wore on, with Robert beating Babos' understudy Gino Coutinho with an effort five minutes from time, following good work from Jermaine Jenas.
