City broke their League Cup duck to secure a spot in the League Cup Third Round draw for the first time in eight years following an entertaining encounter at Whaddon Road.
Republic of Ireland international Glenn Whelan curled home an exquisite free kick early in the second half, before Richard Cresswell doubled the advantage three minutes later with a clinically taken second.
Robins star Ashley Vincent ensured a nervy final 30 minutes though as he halved the deficit with a well taken strike for the hosts just minutes later.
City secured the victory late on though thanks to Jon Parkin who struck home a ferocious effort after good work from Danny Pugh, with a late Alex Russell strike proving to be little more than a consolation.
Tony Pulis rang the changes ahead of the clash making no fewer than ten alterations to the side which dispatched of Aston Villa at the weekend.
The City boss handed first starts of the season to Steve Simonsen, Lewis Buxton, Pugh, Jon Parkin and Vincent Pericard, while Academy starlets Jimmy Phillips and Nathaniel Wedderburn were named amongst the substitutes.
The game kicked off with a typical cup tie feel about it as the League One hosts immediately set out to pressure their Premier League opposition.
Some neat play down the right flank resulted in an early corner for the Robins, but Simonsen came out well to gather the floating ball into the box.
City got some momentum going in the seventh minute and almost took the lead through Cresswell, but his effort was well blocked by the outstretched leg of Alan Wright.
The Potters continued to look the more dangerous and again went close just after the quater hour through Pericard, but the former Juventus man fired wide from 12-yards.
Former Hull striker Parkin was next to try his luck for the Premier League side however his header failed to trouble Shane Higgs in the hosts goal.
The burly striker again goes close several minutes later with a speculative thumping effort which dipped just over the crossbar from 35-yards out.
City's dominance looked to have paid off in the 34th minute as Pericard fired the ball past Higgs and in to the bottom corner, but unknowingly the fourth official had raised his flag for offside.
Former Potter Paul Connor then had the hosts first real effort, but Simonsen was equal to him and gathered comfortably at the second attempt.
Neither side made any changes during the half time interval, and Pulis' decision to stick with his tried and trusted paid dividends as two quick fire goals put the Potters in the driving seat.
Firstly after 50 minutes Whelan curled home a beautiful free-kick after Pericard was upended, then three minutes later Cresswell beat the defender to drill the ball into the back of the net from 15-yards.
To their credit though, the hosts failed to lie down and pulled a goal back immediately after through Vincent, who calmly placed the ball past Simonsen and into the net via the right hand post.
Substitute Dominic Matteo then fouled Connor on the edge of the penalty area; however from the resulting free-kick Ben Gill smashed the ball over the roof of the stadium and into the trees at the back of the stand.
With just thirteen minutes of the game remaining Parkin ensured a passage into the third round was City's with an outstandingly taken first goal of the season.
Late efforts from Andy Lindegaard and Vincent failed to trouble Simonsen before Russell gave the hosts a glimmer of hope with a late goal with just a minute remaining.
His effort proved to be in vain as the Potters secured a spot past the second round for the first time since losing to Liverpool 8-0 at the turn of the century.
