4:32AM BST 05 Aug 2011
Stoke City, who went into the third-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 90 minutes, with Pulis' players seemingly untroubled by the vociferous home supporters at Stadion Poljud.
And the performance was capped in stoppage time as Hajduk defender Ljubo Milicevic put Dean Whitehead's cross into his own net under pressure from Ryan Shotton to make it 1-0 on the night and seal a 2-0 win on aggregate.
Stoke are now a two-legged tie away from the group stages proper, with their name going into the hat for today's draw for the qualifying play-off stage.
This is the first time the club have played in major European competition for 37 years and having been immediately eliminated on the two occasions they competed in the Uefa Cup in the 1970s, it is also the first time they have emerged from a continental tie triumphant - the latest in a string of landmark achievements for the club under the guidance of Pulis, who took over for a second spell as manager in 2006.
''We were quietly confident,'' Pulis said.