The home side took the lead in just the fifth minute when a corner by Alan Judge was turned into the net by Johann Arquin in the six-yard box with the Pompey defence static.
County nearly doubled their lead after 32 minutes when a terrific exchange of passes in midfield put Judge through on the right and his shot was saved by the legs of Mikkel Andersen.
County did make it 2-0 after 47 minutes when the ball fell to Judge 30 yards out after good work by Arquin and he planted a superb right-footed drive into the corner past Andersen's despairing dive.
That man Judge was involved again as County went 3-0 ahead after 57 minutes, playing in Arquin who slipped it past Andersen with ease to seal the victory.
