Smith struck five minutes before the break, driving at the heart of the Chi defence and striking a shot that appeared to go through stand-in ‘keeper Anthony Ender.
Ender was filling in for the unavailable Stephen Mowthorpe in a team that was otherwise unchanged from the one that started the friendly with Worthing at the weekend.
In severely blustery conditions Chi started brightly against their higher-division opponents creating a number of chances early on.
Firstly Kaleem Haitham tested debutant Bognor ‘keeper Durin from long-range, while moments later Callum Overton flashed an effort just wide.
Durin was called upon again in the twelth minute when Josh Clack won the ball back high up the pitch allowing Lloyd Rowlatt the chance to drive at the Bognor defence and draw a good save from Durin.
From the resulting corner Jamie Horncastle missed a golden opportunity to give Chi the lead, breaking free at the far post he could only head against the post from inside the six yard box.
Miles Rutherford’s men would live to rue those early missed chances as the Rocks began to take control of the game as the half wore on.
Striker Jimmy Muitt was at the thick of the action, wasting three chances in quick succession. A good interchange with Smith saw Muitt bear down on goal but under pressure from Connor Cody he could only shoot straight at Ender.
Minutes later he blazed over the bar following a neat cut back by Read then the when presented with the clearest chance of them all after good play again by Smith his effort was smothered by the on-rushing Ender.
Muitt was let off the hook somewhat by striker-partner Smith shortly after though as the pressure finally told and the former Portsmouth man was able to find a way past Ender to give Bognor the lead going into the break.
The second half saw Chi attack into the strong wind and it turned out to be a half of fewer chances for both sides.
Substitute Scott Jones fizzed a shot over the bar from distance, while fellow sub Rory Biggs was denied by a good block as Chi searched for an equaliser.
At the other end Rocks had chances to put the game to bed, Dan Simmonds forcing a good fingertip save from Ender after a poor defensive header by Rob Hutchings.
Chi’s final opportunity came after a good run by Clack saw him reach the byeline, his centre was fumbled initially by replacement ‘Keeper Charlie Searle but with no player in yellow on-hand to convert he was able to gather at the second attempt.
With that Bognor were able to see out the remaining minutes and add the Sussex Community Shield the Sussex Senior Cup triumph back in May.
With Chichester’s pre-season outings now at end attention turns to the Emirates FA Cup tie with Erith Town on Saturday 10 August at Oaklands Park.