The win came despite anÂ abundance of discipline problems for the hosts.
They picked up six yellow cards and two red cards playing most of the second half with 12 men.
Both Greg Hoolihan and Finn Parry were sent off in the second half for collecting two yellow cards apiece.
Portsmouth were guilty of conceding 33 penalties during the game.
Head coachÂ Neil McRoberts felt his side just did not adjust the situation with the way the game was being managed.
He said: '˜It was bizarre and slightly frustrating for us.
'˜We failed to adapt to what the referee wanted in different areas of the game.
'˜In a game we should be looking at conceding 10 penalties or less.
'˜That isn't conducive to performing well and we have to show a bit more rugby intelligence.
'˜Having said that we were fantastic in the opening half hour during which we had already secured a four-try bonus point.
'˜We should have kicked on from there and built up our points difference.'
Jack Easterbrook, Mark Ovens, Tom Hopkins and Sully CauCau notched the early tries.
Daz Leggat added a fifth before half-time with Simon Morgan adding three conversions.
Parry scored Portsmouth's second-half try before the game got ugly.
United Services PortsmouthÂ maintained the pressure on the top three with a 28-19 win against Old Tiffinians at Burnaby Road.
Player-coach Rich Neil felt it was the perfect way to get their derby defeat against Portsmouth out of their system.
He said: '˜It got the monkey of last week's loss off our back.
'˜Our structures were much better.
'˜I was particularly pleased with our scrambled defence against strong opponents.
'˜We worked really hard in that area to get turn-over ball.'
Alex Smith, Owen Herbert, Billy Rolfe and Arthur Robinson scored the home tries.
PetersfieldÂ suffered a 40-7 defeat at Trojans.
In Hampshire twoÂ Southsea NomadsÂ earned an excellent 38-17 win against third-placed Stoneham at Furze Lane.
Home skipper Ben Horrod felt the side showed they had real motivation.
He said: '˜After losing last week the team were determined to put things right.
'˜We took our chances well and our defence was strong apart from a couple of lapses in concentration.'
Horrod crossed twice withÂ number eight Joe Beale, outside-half John Titcombe, Jonathan Branston and Hobson also crossing.