Record Portsmouth signing Diomansy Kamara marked his debut with the only goal at Prenton Park.
The Premiership side did just enough to see off a spirited Tranmere outfit and book their place in the third round of the Carling Cup.
The Merseysiders were not without chances, but failed to convert them and did not put enough pressure on Pompey keeper Jamie Ashdown.
Linvoy Primus was outstanding in the heart of the Portsmouth defence and there were lively contributions from Matthew Taylor and the hard-working Gary O'Neil.
But Andrew Griffin, Primus and David Unsworth all collected cautions.
Mark Rankine excelled in the Tranmere midfield but Rovers lacked the necessary bite upfront.
There were few chances in the opening period although Eugene Dadi saw a shot deflected away for a corner on the half-hour while Jason McAteer was just wide for the home side in the 39th minute when set up by Iain Hume.
O'Neil got in the best effort for Pompey in the 41st minute but his shot was turned away for a corner by John Achterberg.
Earlier the keeper did well to stop Patrick Berger's 25-yard free-kick.
Tranmere missed a great opportunity in the 49th minute when Dadi headed Jason McAteer's cross over the bar.
Then at the other end, Berger fired over when set up by Kamara before putting another effort into the side-netting.
The only goal came in the 65th minute. Berger played the ball back into the path of Kamara from a deep cross by O'Neil and the new man netted with a left-foot shot that went just inside the left-hand post.
Ryan Taylor saw an 83rd minute free-kick held by Ashdown while at the other end Berger fired just wide from the edge of the box.
Tranmere almost forced extra-time in the 90th minute but substitute Calvin Zola headed over in front of a gaping goal after being set up by Paul Hall.