The Stoke striker nodded home a third-minute winner from a textbook Matthew Etherington cross to ensure the club's first foray into Europe since 1974 would not simply pass them by.
Heads up: Jon Walter puts Stoke ahead after three minutes
Walters' early goal separated these two teams but the slender margin of victory did not reflect the home team's dominance.
MATCH FACTSSTOKE CITY (4-4-2): Begovic 6; Wilkinson 7, Shawcross 6, Huth 7, Wilson 6; Pennant 8 (Whitehead 75, 6), Whelan 7, Delap 7, Etherington 8 (Shotton 88); Jones 7, Walters 7. Subs not used: Sorensen, Collins, Pugh, Diao, Woodgate.Booked: Huth.
HADJUK SPLIT (4-5-1): Subasic 7; Oremus 6, Vejic 6, Maloca 5, Lima 6; Tomasov 6 (Ahmad Sharbini 85), Inoha 6, Brkljaca 6, Andric 5, Anas Sharbini 5(Ljubicic 90); Vukusic 5 (Vukovic 63, 5).Subs not used: Kalinic, Kukoc, Dens, Saric.
Man of the match: Matthew Etherington.Referee: Babak Rafati (Germany) 8.
However, Hajduk Split coach Krasimir Balakov followed in the footsteps of several Barclays Premier League managers and observers when he moaned afterwards about the manner of Stoke's play, with Rory Delap's giant throw-ins once more in evidence.
Perhaps there was a clue of Pulis's approach from the hosts' team-sheet. Barring Asmir Begovic starting in place of Thomas Sorensen in goal, Pulis fielded the same side that contested the FA Cup final against Manchester City in May.
The visitors, vastly more experienced in Europe, found themselves penned back by near constant bombardment from the very first whistle. The only blot by the end was that they had not added to Walters' cool header.
Stoke boss Pulis said: 'It was a good night for us. A full house with a great atmosphere and we are disappointed not to have won by more than one goal.
'We had enough chances, especially in the first half. It wouldn't have been an embarrassment if we had come in two or three up. We have dipped our toe in European football and we have nothing to lose in the second leg.'
Colourful: Hajduk Split supporters at Britannia Stadium
But asked about Stoke's style, Balakov said: 'I don't think it's right football. But we had to get used to it. We don't have that style but we had to adjust to the situation and we will have to do so again in Split.'
Pulis smiled when told of the criticism and said: 'Really? I couldn't give a hoot.'
Balakov's words were harsh on the hosts who, with Etherington and Jermaine Pennant patrolling the flanks, can hardly now be described as 'route one'.
Full flight: Stoke's Matthew Etherington takes on Mirko Oremus
It was the former who crafted the goal. Just two minutes and 15 seconds had elapsed when Etherington crossed from the left to Walters, who could have not have asked for a more perfect delivery. The former Ipswich Town man set himself perfectly and headed the ball back across Hajduk keeper Danijel Subasic into the net.
Going close: Defender Robert Huth tries his luck with a shot from outside the box
Kenwyne Jones had an effort ruled out for offside, saw keeper Subasic pull off the save of the night from another header and both he and defender Robert Huth were denied by last-ditch block tackles. It was less impressive after the interval as the home players understandably tired.
In control: Stoke's Kenwyne Jones holds off Srdan Andric
'We will give it our best shot next week,' said Pulis. 'We don't have a match the weekend after so I'll field a strong side.
'Their crowd is nearly as noisy as ours, so it should be a good game.'
The holiday season may be in full swing on the Dalmatian coast, but it seems that the tourists might not be the only ones feeling the heat nextThursday.
Made to wait: Jonathan Woodgate was an unused substitute as the defender awaits his Stoke debut
Woodgate for England! Stoke boss Pulis backs defender to make international returnStoke savouring long-awaited European return with total recallCLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAME