Pompey, who lost manager Steve Cotterill to Nottingham Forest yesterday, started the encounter at Fratton Park slowly and it was visiting Barnsley who created the best chance of the first half when Danny Butterfield's effort struck the post.
The home side came out brightly after the restart and eventually broke the deadlock on the hour mark. Norris was the scorer, taking one touch before volleying past Luke Steele from the edge of the area.
That advantage was doubled just two minutes later when David Kitson crossed low from the right and Varney was on hand to convert at the near post.
Norris and Kitson both had chances to extend the winning margin further but they were unable to breach Steele's net for a third time.