Goals from Reeco Hackett, George Hirst, Aiden O’Brien and Sean Raggett meant Rovers suffered a 4-0 defeat at Fratton Park in Sky Bet League One.
Rovers created the better chances in the first half but failed to capitalise. Joe Dodoo went the closest in the opening period when his shot from close range beat the keeper but was cleared off the line by Raggett.
It took two good saves from Gavin Bazunu early in the second half to deny first Josh Martin and then Tommy Rowe, but Portsmouth clicked into gear on the hour mark. Hackett headed in from close range to put them ahead and four minutes later, Hirst took the game away from Rovers with a cool finish underneath the onrushing Jonathan Mitchell. O’Brien made it three with ten minutes remaining and Raggett - having done his job at one end - headed in a fourth with the last touch of the match.