The Pompey fans that went Fratton Park were rewarded with a rock-solid performance, as Frederic Piquionne, John Utaka, Niko Kranjcar and Richard Hughes fired their side through.
Piquionne opened the scoring when Kranjcar played him in on goal after 20 minutes, taking his time before coolly slotting under Bartlett. Utaka then atoned for his earlier wastefulness after 23 minutes, when Piquionne's cross from the left found him free in the box and he buried Portsmouth's second.
Portsmouth then extended their advantage three minutes before the break, when Kranjcar's low shot from the edge of the box evaded Bartlett's grasp and squirmed home.
Pompey then bagged their fourth goal after 56 minutes when the Bulls failed to clear their lines on the edge of the box. The ball broke to Hughes, who lashed home a superb left-footed effort on his first appearance of the season.
Hereford appeared to be dead and buried at this point, but they were given a lifeline when Tristan Plummer hit home from the spot after he was fouled.