The Potters, who went into the third qualifying round second leg with a 1-0 lead from last week's first leg at the Britannia Stadium, put in an impressively controlled display over the 90 minutes, Tony Pulis' players seemingly untroubled by the vociferous home supporters at Stadion Poljud.
And the performance was capped in the 93rd minute by substitute Ryan Shotton, who was in the right place to convert Dean Whitehead's cross.
Pulis named another strong side for the match, handing a Stoke debut to summer signing Jonathan Woodgate.
The former Tottenham player came into the heart of the Potters defence with Robert Huth switching to full-back to replace Andy Wilkinson, who was not included in the squad.
Rory Delap had not travelled with the group, so Whitehead took his place in midfield in the only other change to the team that had started the first leg.
As anticipated, Stoke received a hostile reception from the raucous crowd as the match got under way and they were soon having to deal with a Hajduk attack.
The hosts' coach Krasimir Balakov had promised his team would be firmly on the offensive and in the fifth minute they looked threatening as Marin Tomasov broke into the box.
Woodgate was on hand to guide the ball out for a corner, which Mario Brkljaca then headed over the bar.
The Potters began to settle, though, and Jon Walters found himself in a good position around the quarter-hour mark but could only lift his shot into the body of defender Ljubo Milicevic.
Protests that Milicevic had handled were waved away by Italian referee Andrea De Marco, who gave a similar response moments later as Kenwyne Jones was sent sprawling in the area.
Ivan Vukovic then tried his luck from distance, driving the effort off target.
There was a moment of concern for Stoke in the 30th minute when Walters went down clutching his leg after a late challenge from Milicevic.
De Marco booked the Hajduk player while a stretcher came on to the pitch, but Walters was soon back on his feet.
Huth sent an attempt high and wide soon after and Jermaine Pennant delivered a cross into the box which was just beyond Jones' head.
Matthew Etherington was next to put the ball in the danger zone, but goalkeeper Danijel Subasic was alert to grab it before Jones could pounce.
The Potters seemed to be in the ascendancy and perhaps as a sign of their frustration, Hajduk picked up another yellow card as Srdan Andric brought down Pennant.
Tomasov fired a shot in towards the end of the first half, but Asmir Begovic caught it comfortably.
Hajduk's fans were growing restless and some bottles were thrown from the stands soon after the restart when Huth tackled Vukovic by the touchline.
Glenn Whelan struck the ball into Subasic's arms before Vukovic was challenged again, this time by Ryan Shawcross, and had to be substituted for Ahmad Sharbini.
Moments later Anas Sharbini advanced into the box and got a shot away which Shawcross managed to divert behind for a corner.
Whitehead became the first Stoke player to be shown a yellow card in the 63rd minute after clattering Ahmad Sharbini, and Shawcross then headed wide from Pennant's corner.
At the other end, Dinko Trebotic scuffed an effort wide before being taken off for Nikola Saric.
Tomasov saw a free-kick deflect the wrong side of the post off Whelan and then hoisted a shot well wide.
With a little under 15 minutes to go, Pulis withdrew Jones and introduced Salif Diao.
Brkljaca then appeared fortunate to escape punishment for an apparent dive in the box.
After Begovic smothered a Tomasov shot, it was Pennant who received a booking for time-wasting, Pulis almost immediately substituting the winger for Danny Pugh.
Walters then came off for Shotton, who was the hero late on as he bundled in Whitehead's cross.
Source: Team Talk
Source: Team Talk