Connor Mahoney and Dean Rittenberg both scored twice, whilst Modou Cham grabbed his third of the season to give Rovers all three points in an impressive display.
Mahoney gave Rovers the lead on the quarter hour but Stoke levelled on 39 through Eddy Lecgyne.
However parity lasted barely three minutes as Rittenberg fired Rovers back in front from the penalty spot after handball in the area.
The second half started badly for Eric Kinder's side as Robbie Parry's strike saw the Potters level once more, but like the first half, Rovers' response was immediate as Rittenberg notched his second of the game from close-range.
Modou Cham deservedly got on the scoresheet to put daylight between the two sides and the worthy victory was confirmed a minute from the end as Mahoney drove home.
Coach Eric Kinder made two changes for the visit of Stoke. With David Raya joining Southport on loan it meant a debut for Ryan Crump in goal, whilst Ryan Tunnicliffe got some game time due to his ineligibility for the first team at Fulham. The midfielder taking the place of John O'Sullivan who joined Accrington Stanley earlier in the day.
After a cagey start it was Rovers who took the lead with the very first attack of the match on 14 minutes.
Full back Jack Doyle made impressive ground down the left before delivering a cross that Connor Mahoney headed home from close-range.
The lead was almost doubled three minutes later when from a Mahoney corner the ball deflected goalwards but a Stoke man was on hand to hack off the line.
Rovers continued to force the pace and again went desperately close to grabbing a second when a thunderbolt from Modou Cham slammed off the crossbar and down onto the line.
Goalkeeper Ryan Crump was called into action for the first time just before the half hour, but after Jack Nardiello broke through on goal the debutant saved well low down. Moments later the 18-year-old made another fine stop, unaware that the flag was raised.
The visitors hadn't threatened too much in the first half but drew level on 39 minutes. As a cross from Curtis Strong deflected off Mahoney it bounced off the crossbar and behind. The resulting corner was only cleared as far as Eddy Lecygne and the Stoke man hit the ball through the crowd and into the bottom corner of the net.
But no sooner had the Potters drawn level then Rovers were back in front. Another Jack Doyle centre caused problems and as Hyuga Tanner closed in a Stoke defender handled and the referee pointed to the spot.
Dean Rittenberg stepped up and made no mistake from 12 yards, emphatically finding the net via the underside of the bar for Rovers to lead at the break.
However their advantage barely lasted 30 seconds as Stoke scored immediately from the restart. Robbie Parry taking full advantage of the space afforded to him as he ran through to blast home from ten yards.
But just as the first half, the response was immediate. Rovers attacked from the kick-off down the right to where Mahoney centred for Rittenberg and the England youth international lashed home his second of the game to put the home side back in front.
Nardiello fired just wide on the hour mark as the visitors looked to draw level a third time, but it was Rovers who grabbed the crucial next goal to put daylight between the two sides thanks to a third goal of the campaign for Modou Cham.
The wideman had earlier been thwarted by a fine stop by Dale Eve but on this occasion he wouldn't be denied, arriving at the back post to dispatch Rittenberg's centre with aplomb.
Ryan Tunnicliffe got a hardworking 66 minutes under his belt, playing just in front of the back four, the loanee kept play ticking over for the Blues.
Rovers were comfortably seeing out the match but there was still time for them to add a deserved fifth. It came thanks to the persistence of Mahoney, taking advantage of defensive hesitancy to steal the ball and slot home and clinch the win.
ROVERS: Crump, Daly, Doyle, Tanner, Lavelle, Lenihan, Mahoney (sub Joel 89 mins), Bauress (c), Rittenberg, Tunnicliffe (sub Carson 66 mins), Cham (sub Preston 75 mins).
Subs not used: Williams, Paulo Jorge.
Goals: Mahoney 14, 89 mins, Rittenberg 42, 47 mins, Cham 68 mins
STOKE CITY: Eve, Wheeler, Strong, Lecygne (sub Waring 67 mins), Coulson, Watkins, Parry, Shenton (sub Monlouis 57 mins), Skapetis, Ward, Nardiello.
Subs not used: Gyollai, Barber.
Goals: Lecygne 39 mins, Parry 46 mins
Booked: Wheeler, Lecygne, Parry.