Ronan Curtis got the only goal of the game at Fratton Park to officially relegate the winners and, temporarily at least, lift the Blues back into the top six.
It was a promising display from Danny Cowley’s men with football which was easy on the eye at times, particularly in the first half.
John Marquis had a great chance to get on the scoresheet after the break before Curtis went close to a second as Pompey ended their four-game winless run.
And it was a win they warranted with George Byers shining as Cowley sprung a surprise with a switch to a 3-4-3 formation.
It was a high-energy opening in the spring sunshine at Fratton Park, but there was little in the way of clear openings before Alex Rodman angled a drive just wide for the visitors in the 26th minute.
The response was for Pompey to open the scoring a minute later as a moment of real quality from Byers freed Curtis in the box and the Irishman dispatched his low finish past Anssi Jaakkola.
Rasmus Nicolaisen nearly doubled the lead seven minutes later when he headed just wide from Ben Close’s ball in.
There was a goal-saving touch from Raggett at the end of the half with James Daly poised to apply the final touch a couple of yards out.
Rovers started well after the break without having clear openings, before Marquis wasted a big chance for the second as he allowed a block to come in after being put free on goal by Curtis.
Pompey were largely comfortable, however, as they saw out the game for a much-needed three points.