Pitman showed his predator instincts in front of goal in the 35th minute, building on his hat-trick at UCD and match-winner against the Hawks.
Eoin Teggart gave the Blues – whose team was made up of first team and academy players – the lead midway through the first half, while ex-Fratton Park striker Dan Smith netted for the Rocks.
Pompey had the first real sight on goal in the 13th minute. Andy Cannon stole possession near the edge of the Bognor box before cracking a right-footed shot which bounced off the crossbar.
The visitors would break the deadlock five minutes later, however.
Keeper Alex Bass’ long clearance was latched on to by Teggart. He jinked his way past a couple of defenders before coolly slotting home from inside the area.
The Northern Ireland youth international should have had a second on 25 minutes. Leon Maloney’s cross was cut out only as far as Pitman, whose effort hit the bar before Teggart scuffed the rebound wide.
The Blues would hit the woodwork for a third time in the 33rd minute. Again, Cannon's tenacity won his side the ball in a dangerous area before Pitman’s dinked shot clipped the frame of the goal.
Pitman would double the away side’s advantage 10 minutes before the interval, though.
Haji Monga cleverly slipped in the captain down the right and he rifled an angled drive into the far corner.
It took Bognor just two minutes into the second half to reduce the arrears – with former Pompey striker Smith on target.
Bass produced an excellent point-blank save to keep out Stuart Green’s header, but Smith was first to react to nod home into an open net.
With Pitman and Bryn Morris not featuring after the break, replaced by academy duo Harry Anderson and Ethan Robb respectively, the Rocks started to take the upper hand.
Smith must have thought he'd notched the hosts' equaliser in the 73rd minute when he was played through one-v-one with Bass but the stopper produced an outstanding save to his right.
Three minutes later, Christian Burgess had the opportunity to restore Pompey’s two-goal lead when he rose highest to meet Cannon’s corner but headed narrowly wide.
In the closing stages, Bognor went close to snatching an equaliser when Simmonds met a cross from the right but Burgess did brilliantly to block the effort and ensure the Blues maintained their 100-per-cent record in pre-season.
Pompey are back in action on Saturday when Kenny Jackett’s first team travel to Stevenage.