Matt Harrold headed the home side in front in the 11th minute and doubled the advantage with a 22nd minute penalty after Mustapha Carayol was brought down.
Andy Dorman swept home a stunning volley from Harrold's 29th minute cross before Kevin McIntyre's in swinging corner deceived Scott Bevan to make it 3-1.
Substitute Matt Lund volleyed in another Carayol cross after 58 minutes to settle any doubt about the outcome and added the fifth with a low drive on 73 minutes.
The convincing win followed Rovers' 7-1 demolition of Burton Albion in their previous game at the Memorial Stadium and things are looking bright for the future under Mark McGhee.
.Accrington contributed to a richly entertaining game and Bevan had to make a brilliant 56th minute save from Padraig Amond's header.