Brett Pitman scored the winner for the Blues on 66 minutes, after seeing his penalty kick hit the post before the hour mark.
'Is proving one hell of a signing.... A real livewire' - Portsmouth match ratings from 2-0 win at Cheltenham
Portsmouth transfer news: Blues receive bids for former Luton and Millwall midfielder
Transfer gossip: Portsmouth eye raids for ex-Chelsea man and Charlton Athletic's former Wigan Athletic midfielder
Portsmouth boss Danny Cowley hails squad depth as tactical masterclass at Cheltenham pays off
Cheltenham 0-2 Portsmouth: Colby Bishop steals show as Blues prove too hot to handle in impressive display at sun-soaked Whaddon Road