Pitman took five minutes to get on the scoresheet as the Blues picked up a 2-0 warm-up win at Nyewood Lane.
And he rounded off an often laboured Pompey display with his second four minutes from time.
The 29-year-old was partnered up front with Conor Chaplin as Kenny Jackett went with a 4-4-2 formation.
And he made an early breakthrough as Chaplin cashed in on Sami El-Abd’s poor backpass and teed up his strike partner to roll the ball home from six yards.
The Blues failed to create the number of opportunities they’ve produced in their other pre-season games to date.
And too often the final pass, cross or decision was off-kilter as they continue their preparations for the League One campaign.
Carl Baker and Rocks striker Ollie Pearce both had shots saved in the first half, as did Adam May before the break.
Danny Rose and Kyle Bennett had opportunities after the interval, before new keeper Luke McGee saved superbly from Tommy Scutt with 14 minutes left.
Then Pitman dinked home a second with four minutes left on an afternoon when Pompey were worked hard by the Rocks.