After 37 years of waiting Stoke City announced their return to European football with a slender but precious victory over Hajduk Split to set up an intriguing second leg next Thursday in Croatia, where the atmosphere promises to be every bit as raucous as the din inside the Britannia Stadium.

A goal from Jon Walters inside three minutes gave Stoke the perfect start and one that they might regret failing to build on depending on the outcome next week. Kenwyne Jones wasted a wonderful chance to add a second goal and Ryan Shawcross had a glancing header cleared off the line from one of a number of Rory Delap throw-ins that caused consternation in the visitors' penalty area.

Not that a Stoke victory in Europe – the only previous one was in 1972, against Kaiserslautern – should be viewed with any disappointment. This was a momentous occasion for Tony Pulis and his players and the fact that Stoke won, kept a clean sheet and got under the skin of the Split manager with their set pieces meant this was a highly satisfactory evening's work.

"I don't think it's right football," said Krasimir Balakov, the Split manager, reflecting on the sight of Delap hurling the ball deep into the area time and again.

"I don't give a hoot, like I don't with anyone else," said Pulis, when told of Balakov's comments.

One thing is for sure, Split can expect more of the same when Stoke go to Croatia. They never looked comfortable dealing with Delap's missiles and the only surprise was that none of his throw-ins yielded the second goal that would have made the scoreline look so much better.

"We're disappointed we never won it by more goals, especially first half – we had enough chances to come in more than one up," said Pulis. "But we've kept a clean sheet, which is important. We'll go to Split and, if we score a goal, they'll have to score three to beat us."

The Stoke manager showed that he was taking the competition seriously by picking a full-strength side – he selected the same team that lined up for the FA Cup final with the exception of Asmir Begovic in goal – and was rewarded with an early breakthrough. Delap swept a superb pass out to Matthew Etherington and the winger delivered an exquisite cross towards the back post where Walters, nodding the ball back across goal and into the far corner, executed a text-book header.

Jones could have doubled their advantage in the 34th minute but Danijel Subasic scrambled the striker's tame header to safety and moments later Hrvoje Vejic hacked Ryan Shawcross's effort off the line.

Split offered little in response and it was not until an hour had gone that Begovic had a serious save to make. The Stoke goalkeeper will surely be busier in the second leg. "This is the first time we have dipped our toe into European football and we'll relish going there," said Pulis. "It's going to be very difficult. Apparently their crowd is nearly as noisy as ours."