Plucky Millwall kept their Championship superiors at bay until a Marvin Elliott own goal eight minutes before the final whistle broke their resolve.
And City, having played one less game through the congested festive period, turned the screw at the death before Ricardo Fuller fired in his second goal in seven days.
Despite the Potters' Championship superiority it was the Londoners who seemed the more enthused by the prospect of fourth round progression.
And they should have taken their first step to Sunday's draw early in the first half, when, in honesty, distinguishing the Premiership hopefuls from the League One strugglers was a puzzling task.
The Lions twice went close to breaking the tedium of an uninspiring opening half hour in which Stoke were content to see their travelling counterparts take the initiative.
Steve Simonsen was forced into action on the seventh minute to deny Neal Ardley his first goal as a Millwall player, tipping over a wonderfully hit 25-yard volley.
But whilst the stopper was to be commended for his agility early on, his side were almost trailing minutes later when he failed to assert himself in the air.
The City number one should have made a routine collection from Maurice Ross' lofted centre, but was caught off his line to watch the ball sail inches wide.
Stoke came into the bout on the half-hour mark and should have entered the interval with a lead to defend were it not for a lack of composure in front of goal.
Mamady Sidibe and Vincent Pericard navigated a way to the touch-line before the latter crafted an incisive ball back to the lurking John Eustace.
But the midfielder, making his first start this campaign, scuffed his shot into the grateful arms of Lenny Pidgeley when the net was the more visible target.
Fuller joined the fray on the restart and the introduction of a third striker began to carve real in-roads for the re-invigorated hosts.
Ross was twice called on to thwart Pericard's attempts of a rare appearance on the score- sheet before the striker riffled low and wide from inside the box.
With City firmly in the driving seat and with a player named Rooney closing down on goal the Britannia Stadium seemed certain to be celebrating the evening's first goal.
But Adam Rooney, not Wayne, introduced on the 73rd minute, collected a Danny Higginbotham through ball before sending the tie's clearest chance narrowly wide.
But Millwall finally crumbled when Higginbotham's drive took a deflection off the hapless Elliott past the rooted Lions stopper.
Fuller doubled the visitors' woes five minutes later when he squirmed through the visiting back-line before chipping the advancing Pidgeley.