Jonathan Walters' strike two minutes into the second half condemned Rovers to defeat once again at the Britannia Stadium.
After a first half which saw the home side just edged proceedings, Rovers were caught cold at the start of the second when Matthew Etherington threaded the ball through to Walters who applied the finishing touch.
Against a defensively strong Stoke outfit Rovers struggled to carve out any clear cut chances in a disappointing display which saw them fail to build on last week's win at Blackpool.
Stoke should have added further goals but Robinson denied Etherington whilst Kenwyne Jones and Ricardo Fuller missed late chances for the home side.
Sam Allardyce had made just the one change from the side that started in the win over Blackpool last time out.
That change saw last week's matchwinner Brett Emerton come into the starting line-up for the first time in the league this season, Niko Kalinic being the man to make way with Mame Biram Diouf leading the line supported by Emerton on the right and El-Hadji Diouf on the left.
Stoke made three changes from the side that defeated Newcastle United last weekend, Jermaine Pennant, Abdoulaye Faye and Rory Delap all returned to the starting eleven.
Despite the statistics that Stoke are the second worse side in the first half and Rovers the third best, it was the home side that started this encounter the brighter.
After just five minutes Kenwyne Jones was inches wide for the Potters, Dean Whitehead catching out Phil Jones to feed the Stoke striker, but his powerful left-footed drive went just past the post.
Five minutes later and Stoke would go closer, a long throw from Rory Delap saw Paul Robinson rush out to watch the ball sail past and bounce off the foot of the far post. A let-off for the Rovers number one.
Rovers came back into the game and on the quarter hour saw a shot cleared off the line. El-Hadji Diouf sending in a teasing ball that Thomas Sorensen in the Stoke goal could only palm away, Brett Emerton hit the ball back goalwards on the volley but Ryan Shawcross was in the right place to clear.
Robert Huth saw yellow for a late lunge on Morten Gamst Pedersen, whilst Gaël Givet saw likewise for his late challenge on Jermaine Pennant as the tackles started to fly.
Whilst Rovers threatened from corner kicks it was the home side who were getting their shots away. Matthew Etherington, saw often a threat against Rovers, hit one effort into the side-netting, Paul Robinson denying the former West Ham man a minute later at his near post.
Rovers weren't without chances of their own as the first half drew to a close, concerted pressure in the Stoke penalty area saw the ball drop to Phil Jones but once again Shawcross was there to make the vital block.
The Rovers fans will have barely returned to their seats when their heroes found themselves a goal down immediately after the restart.
It was a goal of simplicity, a flick on from Kenwyne Jones, a slide-rule pass from Matthew Etherington and a neat finish from Jonathan Walters who outpaced Chris Samba to curl the ball into the far corner of the net for his first Premier League goal.
90 seconds later and the lead was almost doubled, Chris Samba stooping to head the ball off the line from Pennant's centre.
Stoke's quick fire start to the second half saw Sam Allardyce waste little time in making a change. El-Hadji Diouf, whose earlier booking will no doubt have influenced the change, was replaced by Martin Olsson in a like for like switch as the Swede took up position on the left flank, although Rovers did switched to a 3-4-3 formation.
However it was still the home side creating, Robinson denied Etherington from a 25 yard free-kick, then saved well to stop the winger adding a second, the Rovers 'keeper claiming the ball at the second attempt.
Chances for Rovers were few and far between, Olsson's fine touch and cross couldn't be capitalised upon by a sliding Emerton, the Australian putting the ball wide of goal on 70 minutes.
Benjani was introduced for the final 15 as Emerton made way but it was the home side who continued to carry more threat. Again it was Etherington who created the danger when a telling cross found Kenwyne Jones, but his downwards header flashed wide.
A quick free-kick from Salgado two minutes from time could have caught Stoke napping, but Chris Samba's nod down bounced away to safety, it summed up Rovers' afternoon.
STOKE CITY: Sorensen, Huth, Shawcross (c), Faye, Collins, Pennant (sub Fuller 77 mins), Whitehead, Delap (sub Whelan 90 mins), Etherington (sub Wilson 90 mins), Walters, Jones.
Subs not used: Begovic (GK), Higginbotham, Gudjohnsen, Tuncay.
ROVERS: Robinson, Salgado, Samba (c), Nelsen, Givet, Nzonzi, Emerton (sub Benjani 75 mins), Jones, Pedersen (sub Hoilett 86 mins), EH Diouf (sub Olsson 54 mins), MB Diouf.
Subs not used: Bunn (GK), Kalinić, Andrews, Chimbonda.
Booked: Huth, Delap (Stoke City), Givet, EH Diouf, Nzonzi (Rovers)