Stoke advanced to the Europa League qualifying play-offs after a late own goal ended Hajduk Spilt's challenge.
The Potters threatened to add to their first-leg lead as Jonathan Walters broke free, but he had his weak shot blocked by defender Ljubo Milicevic.
The hosts applied more pressure in the second half with Anas Sharbini and Dinko Trebotic both looking dangerous.
But Stoke could relax once Milicevic turned Dean Whitehead's cross into his own net with Ryan Shotton lurking.
A two-legged play-off, with matches to be played on 18 and 25 August, now lies between Tony Pulis's side and the group stages proper.
The Stadion Poljud crowd provided a raucous backdrop to Hadjuk's efforts to drag themselves back into the tie, but ultimately they left disappointed.
Stoke summer recruit Jonathan Woodgate was pressed into early action on his debut, ushering the ball behind as Mario Tomasov broke into the box.
A clever run from Walters briefly bought him space in the Hajduk box, but his ambitious attempt to lift the ball into the far corner was snuffed out by the covering Milicevic.
The home side struggled to open up Stoke's well-drilled backline though, and it was not until the second half that they caused the visitors some nervous moments.
Ryan Shawcross stretched to divert Shabini's effort behind, before goalkeeper Asmir Begovic smothered Tomasov's effort.
As they continued to toil in vain, Hadjuk's ambitions were reduced to trying to force extra time, before that too disappeared in the first minute of injury time.
As in the first leg, Pulis brought on centre-half Shotton as a makeshift forward late on and the 22-year-old's presence in the six-yard box unsettled Milicevic into slicing past Danijel Subasic.