Pitman sidefooted in from a few yards after Conor Chaplin had intercepted a Sami El-Abd pass back to Dan Lincoln five minutes in as a large crowd enjoyed seeing these teams meet for the fifth summer running.
But if that was a poor start to the afternoon for the Rocks, they recovered well to give Pompey a run for their money and make this the Blues' toughest pre-season test to date.
Pitman made the win safe with another close-range effort four minutes from the end, but in between the teams largely cancelled each other out.
Jackett's men arrived at Nyewood Lane having won 3-0 at Salisbury, 6-0 at Havant and 6-3 at Poole - but they found it harder to dominate against a hard-working Bognor side containing the bulk of last season's squad plus a few youngsters out to force their way into the Rocks team for the National League South campaign.
This was a game that had been initially arranged for a midweek date, then called off, then put back on for this mid-summer's Saturday afternoon. It had been called off by Bognor when Pompey admitted they may send only a youth team plus a couple of senior pros. But the clash was on again when Pompey were left with a blank Saturday after having to postpone their visit to Eastleigh over an unsuitable pitch.
Bognor and their fans were delighted to have the game back on and a large crowd filed into the ground for the 1.30pm kick-off - estimated to be around 1,800 - and were pleased to see a full-strength Blues side named, including two new signings making their debuts, Pitman and keeper Luke McGee.
The Rocks were pleased to welcome keeper Dan Lincoln back into the side. Last year's player of the season is still hoping to get fixed up with a club higher up the pyramid but is happy to turn out for Bognor at the moment. Fans are hoping they might see another season of him in a Rocks shirt.
Also in the starting XI were trialists left-back Tom Bird, attacking midfielder Pat Suraci and Joe Lea, a central midfielder.
Lea was in Southampton's youth set-up from the age of nine and was a scholar with them but was released at 18. He went to Yeovil last year and played in a League Cup tie with Everton before going on loan to Gosport for second half of the season. Suraci came through the youth system at Bournemouth, while Bird has played for Hampton & Richmond, Basingstoke and Gosport.
When the game got going under grey skies, Conor Chaplin was first to try his luck, beating Lincoln with a powerful left-footed drive from 25 yards that wasn't far wide.
It took just five minutes for Pompey to take the lead but Bognor had only themselves to blame. The defence dallied when they should have cleared and skipper Sami El-Abd's pass back to Lincoln was short. Chaplin nipped in and square to the unmarked Brett Pitman, who could hardly miss - an early gift on his Blues bow.
It might have been two a minute later as Chaplin and Danny Rose set up Carl Baker but his drive across goal was well palmed away by Lincoln. Ollie Pearce had Bognor's first shot at goal, forcing McGee into a save with a long-range attempt.
Pearce almost seized on hesitancy in the Pompey defence on 14 minutes but couldn't get the ball under control quickly enough for a shot. Gareth Evans had the Rocks on the back foot on 24 minutes with a surge down the right but his dangerous ball into the six-yard box was dealt with by Chad Field. There was more danger when Pitman flicked on a Baker corner at the near post but there was no-one there to convert it.
Lincoln had to palm a Bennett cross away as Baker lurked, and Burgess headed over from one of numerous corners Kenny Jackett's side won. The Rocks won their first corner on 32 minutes after good work by Tom Bird and Pearce down the Bognor left.
A cross by Tareiq Holmes-Dennis saw Chaplin set up Adam May for a chance a minute before the break but Lincoln blocked him from close range. Then Evans found space for a low curling shot that was bound for the bottom corner but was pushed clear by the keeper.
The Rocks made five changes at the start of the second half. Calvin Davies, Jimmy Muitt, Corey Heath, Kieran Rowe and Dan Beck came on. Off came Whyte, El-Abd, Lee, Wild and Parsons. Two of the subs - Muitt and Davies - combined to put Pompey under pressure three minutes into the half but Davies' cross was cleared.
Bennett bought himself space for a low 25-yard shot on 54 minutes - it beat Lincoln but went inches the wrong side of the post. The match continued at a fairly pedestrian pace - perhaps not surprising for a mid-July friendly.
Burgess headed a corner straight at Lincoln before another Bognor change - Tommy Scutt replacing Suraci on 63 minutes. Pitman almost met a Bennett cross from the left but was put off by sub Heath's challenge.
Tommy Block replaced Field on 72 minutes although the Rocks had wanted to bring El-Abd back on for him - but were not allowed to by the officials, which seemed odd on a day when Bognor had changed almost the whole team between half-time and early in the second half.
Ex-Fratton youngster Scutt looked like he must equalise with 16 minutes left but his close-range volley was beaten away superbly by McGee. Immediately at the other end Lincoln made a save that was just as good - fingertipping a Pitman flick over the bar after a corner.
Bognor's final change on 82 minutes saw Lorenzo Dolcetti replace Pearce.
Pitman doubled his and Pompey's tally with four minutes left, converting when Baker found him unmarked with a chipped pass into the area.The ex-Ipswich and Bournemouth striker had thoughts of a hat-trick two minutes later when Chaplin's cross almost found him but it was just too high.
Rocks: Lincoln, Whyte, Bird, Tuck, El-Abd, Field, Parsons, Lea, Wild, Pearce, Suraci. Subs: Heath, Muitt, Block, Scutt, Rowlatt, Beck, Dolcetti, Davies.Pompey: McGee, Evans, Burgess, Davies, Holmes-Dennis, Baker, Rose, Bennett, Chaplin, May, Pitman. Subs: Bass, Talbot, Whatmough, Lalkovic, Close, Main.Ref: Gary Parsons
See the Bognor Observer on Thursday for reaction to the game and all the latest from Nyewood Lane