The Rocks were 2-0 down at half-time but pulled a goal back early in the second half through ex-Pompey academy striker Dan Smith and came close to pulling level.
They dominated parts of the second half and coach Robbie Blake ended up delighted with their endeavour and the way they took the game to their professional visitors.
It was the seventh year in a row Pompey had sent a team to Nyewood Lane for a pre-season friendly – and it has become an important date in the Rocks calendar and a big fundraiser for them. On this occasion it looked like there were well over 1,000 in the ground.
Pompey included Brett Pitman, Christian Burgess and Andy Cannon in their starting XI as well as forward Leon Maloney, who spent part of last season on loan at Bognor.
The Rocks team was similar to the one that started against Havant last week – the first Bognor friendly of the summer which they lost 3-1 – but left-back Ashton Leigh was back sooner than expected after injury and his brother Tommy was in the centre of defence after a goalscoring debut against the Hawks.
Two ex-Pompey academy youngsters – Smith and Freddie Read – were also in the Bognor starting line-up and there was another chance for keeper Charlie Searle to impress, with no sign of Dan Lincoln returning for another season between the sticks..
The sun was beating down as a large crowd boosted by hundreds of Pompey fans packed into the Lane. The final figure was reckoned to be close to 1,400.
It was a fairly pedestrian start to the game with both sides passing it around neatly but not penetrating. The Rocks were first to find a couple of dangerous-looking crosses, and the game's first corner, but there was no-one to get on the end of any balls into the box.
Pompey came to life and Cannon struck Searle's bar with a fierce drive from 20 yards out on 14 minutes. The keeper was relieved to see it bounce back out.
The Blues, who were being directed from the touchline by assistant boss Joe Gallen but with manager Kenny Jackett alongside Stuart Pearce in the stand, looked like they were starting to come to life and Brandon Haunstrup - another in the Pompey squad who has had time on loan at Bognor - went on a powerful run down the left that came to nothing.
Jimmy Muitt almost set up Stuart Green on 20 minutes with a diagonal ball into the box but he was offside. A minute later Pompey were ahead when youngster Eoin Teggart cutting in from the right and curling a shot beyond Searle.
They almost doubled their lead five minutes later when Maloney weaved his way into the six-yard box. When he was thwarted by a tackle it fell to Brett Pitman, whose delicate lob came back off the bar and Bognor scrambled it away. Pompey, after a slowish start, were now looking by far the more dangerous team.
A purposeful run at goal by Smith was halted by a timely tackle by Matt Casey. Pitman tried one from 25 yards but James Crane got in the way. A minute later Pitman found space again to loft a shot towards the top corner but with Searle nowhere, it came back off the crossbar once again.
It was all Pitman and it was no surprise to see him bury the Blues' second on 35 minutes after being played in on goal by a Haji Mnoga pass with the Rocks defence watching.
Mnoga sent a low shot skidding towards the bottom corner with a couple of first-half minutes later but Searle was equal to it.
Pompey brought on Harry Anderson and Ethan Robb for the second half in place of Bryn Morris and Pitman – the latter's removal good news for the overworked home defence.
Suddenly the Rocks were back in it three minutes into the second half when Smith converted a chance from close in. The opening was created by a sublime pass from Doug Tuck to Whyte, whose cross fell to Green - and his header forced a save from Alex Bass that Smith followed up to net.
Bognor had their tails up and, buoyed up by their breakthrough, went close to an equaliser through Muitt.
Ashton Leigh was replaced by another Bognor debutant, Gibraltar under-21 international Jack Breed, on 55 minutes. More changes followed as another friendly became disjointed with all the comings and goings.
Emmett Dunn and Tommy Scutt replaced Tuck and Read for the Rocks while Harry Cavanagh came on for Gerrard Storey for the Blues.
Bognor's fine spell of pressure at the start of the second half had rather blown itself out but they were still giving a good account of themselves.
Smith ought to have doubled his tally and drawn Bognor level on 73 minutes when he was played through by sub Scutt but Bass was quickly out to block him.
Bognor continued to hunt for an equaliser and Smith had another chance in the air after Scutt's cross was not dealt with, but he couldn't direct it towards goal.
More subsitutions followed – Anderson was replaced by Alfie Stanley for Pompey, while Charlie Williamson replaced Green for the Rocks. Then George Bingham replaced Keaton Wood. And yet another change … Liam Brady on for Muitt for the Rocks.
A rare Pompey attack in the final minute of the 90 ended in Teggart drifting a shot just over Searle's crossbar.
Bognor kept going until the end and Brady almost made an opening for himself in the box but was denied by Burgess' well-timed tackle.
Rocks: Searle, Crane, A Leigh, Tuck, T Leigh, Wood, Whyte, Read, Smith, Muitt, Green. Subs: Scutt, Dunn, Breed, Bingham, Brady, Simmonds, Williamson.
Pompey: Bass, Haunstrup, Mnoga, Morris, Casey, Burgess, Cannon, Storey, Pitman, Teggart, Maloney. Subs: Durin, Stanley, Hancott, Cavanagh, Dandy, Anderson, Robb.
Ref: Dan Austin
* Next up for Bognor is a boot-camp style training visit to the FA's St George's Park this weekend which will include a friendly against another non-league club. Then it's off to Horndean to face Michael Birmingham's Wessex League team next Wednesday.