Winger Noah Cannon scored two tries as the home side recovered from a slow start.
Portsmouth showed their scrummaging power right from the start, pushing the Bromley pack back in the first scrummage.
But the Kent side retained possession and pushed the home side back in the opening stages.
Midfield pressure paid off for the visitors as they took a sixth minute lead '“Â the home midfield defence was sliced open and Jonathan Griffiths took a good offload to score near the posts.
Stephen Pillow added the conversion.
Midway through the half the home forwards started to put the visitors under increasing pressure.
This paid off when the home side kicked two penalties to the corner and hooker Tim Snowdon was driven over.
Soon after a superb move from the home three quarters put the hosts in front.
Simon Morgan made the initial break and linked with Mark Ovens who putÂ winger Noah Cannon in for the try.
Morgan added the extra points to give Portsmouth a 12-7 lead at half time.
Conditions had improved a little at the start of the second period, after the thunderstorm and torrential rain of the first half.
Portsmouth resumed the stronger and soon stretched their lead.
A powerful drive took the home side up to the Bromley line and Morgan was provided with quick ball.
The scrum half passed to Rhys Bowen who put Ovens in at the corner.
An excellent Morgan conversion from wide out stretched the home sides lead to 19-7.
Poor discipline saw a penalty advanced 10 metres and allowed Bromley to cut the deficit to nine points.
The home sides response was immediate with a thrilling break out try, cuttingÂ through from half way and winger Cannon took the scoring pass.