Tranmere were a shadow of the side which had whipped Coventry in the Worthington Cup in midweek as they suffered their second home League defeat.
Portsmouth were ahead after only 60 seconds and were assured of their first away win by the 48th minute when they took a four-goal lead.
The Tranmere defending at times was woeful and a five star performance in midfield by Alan Mahon failed to rub off on his colleagues.
Stefani Miglioranzi was the playmaker for Pompey and there was also some excellent work from Alan McLoughlin, Michalis Vlachos and Frenchman Jeff Peron.
Peron headed home from a cross by Mike Panopoulous after one minute and added a second in the 17th minute with a neat lob over keeper John Achterberg after a clever interchange with John Durnin.
Tranmere failed to control the ball well enough in the difficult windy conditions.
The visitors went three-nil ahead in the 39th minute with Guy Whittingham heading home after mix up between Steve Yates and the keeper.
The Merseysiders put the emphasis on attack after half-time but fell four goals behind within three minutes of the restart.
Yates failed to clear a cross by Matthew Robinson. Panopoulous hit a post with his first shot but netted from the rebound.
Andy Petterson made a good stop from Andy Thompson after 55 minutes but Portsmouth remained in control until the closing minutes.
David Kelly finally headed a goal for Tranmere in the 82nd minute from a cross by Michael Black.
Then in injury time Dave Challinor headed a second from a free-kick by Lee Jones.
Peron and Panapoulous collected cautions for Portsmouth but it was a pleasing display by Alan Ball's outfit.