The Rocks were reduced to 10 men in the first half after Calvin Davies received a straight red, before Dan Beck (OG) scored the only goal of the game.
Meanwhile, in the Southern League east division, Moneyfields beat Chalfont St Peter 2-1.
Dan Wooden scored twice for Moneys in quick succession after the visitors went behind.
Elsewhere, in the Wessex League premier division, AFC Portchester drew 2-2 at Alresford Town after conceding late on.
Denver Hume: Portsmouth's expensive forgotten man and why former Sunderland defender really could be one for the future
'We wanted to show him a bit of love' - Portsmouth-based Spurs fans' terrific gesture to ensure Dane Scarlett feels at home on the south-coast
League One latest: Portsmouth linked duo set for Oxford United and Lincoln moves, Southampton prospect joins Blues rivals as Ipswich land former Blackpool and Derby veteran
'Real driving force... lion-hearted display... classy presence' - Neil Allen's Portsmouth ratings from 3-0 Carabao Cup win at Cardiff
'We’ve got a real problem': Portsmouth boss reveals headache after career first at Cardiff
The home side took the lead in the first two minutes.
But poor defending saw the Royals score two goals in as many minutes.
But there was late drama after Alresford scored from a corner to make it 2-2 in the 90th minute.
Petersfield won 2-0 in their game against Cowes Sports.
Goals by Dan Thompson and Jordan Geddes gave them all three points.
Horndean’s game against Sholing was called off due to the weather, along with Fareham’s match against Blackfield & Langley.
Baffin Milton Rovers’ game at Amesbury Town was also postponed.