It was their first away win since October and cements their position in the top ten - leaving them just seven points off the play-off places.
The Rocks took the game to their hosts right from the opening, creating several good chances in the first ten minutes.
The pressure paid when Harvey Whyte gave Bognor the lead on 15 minutes. Whyte jumped highest above the VCD defenders to tuck his header beyond Nick Blue.
The only real chance for the hosts was from a Lee Dawson free-kick that didn’t trouble Chris Winterton in the Bognor goal.
Rocks continued to apply pressure on the home side and deservedly got a second just before the half-hour mark.
A great pass from Alex Parsons was cleverly flicked into the net by Stuart Green.
Bognor could have gone 3-0 up but Craig Robson’s header was well held by Blue.
Towards the end of the half, the hosts managed to relieve some of the pressure and give the Bognor defence a few more problems.
But the visitors looked comfortable going into the break with a two-goal lead.
Five minutes into the second half a first-time volley from Doug Tuck looked goal-bound only for Blue to produce a first-class to deny the Rocks man.
VCD had a bit more urgency to their play in the second half, putting pressure on the Rocks defence.
The hosts pulled a goal back on 55 minutes when a sweetly-hit volley from Aaron Jeffery found the back of the net.
Bognor weathered the storm, though, and then created several chances of their own.
On 71 minutes Ollie Pearce was put through on goal, only to be brought down in the box to win a penalty. Pearce brushed himself off to confidently regain Bognor’s two-goal lead.
BOGNOR: Winterton, Whyte, Crane, Tuck, Woodford, Robson, Green, Thomson, Prior, Pearce, Parsons. Subs: Sackman, Oatway, Lawson, Cody.