A young Welsh side battled throughout as John Toshack starts to plan for the future and he was not let down by any of his players.
His starting line-up had an average age of only 25 and Wales were under pressure from the first whistle with new Tottenham striker Grzegorz Rasiak going close with a header and Miroslaw Szymkowiak firing just over in the opening minutes.
Zurawski's 30-yard shot was then deflected inches wide as Poland started brightly.
When Wales settled Rob Earnshaw fired straight at Artur Boruc while at the other end Zurawski's shot was fumbled by Danny Coyne but the Wales keeper survived.
Poland continued to dominate after the interval and Zurawski's clip almost broke the deadlock before the hosts were awarded a penalty.
Kamil Kosowski was brought down by Richard Duffy in the 54th minute and Zurawski fired past Coyne to make it 1-0.
As Wales pushed for an equaliser Ryan Giggs had a 25-yard free-kick saved by Boruc in the closing minutes but Poland held on to clinch the three points that take them to Germany.
Poland: Boruc, Jop, Rzasa, Baszczynski, Kosowski, Bak, Sobolewski, Smolarek, Zurawski, Szymkowiak, Rasiak. Subs: Kowalewski, Mila, Zewlakow, Frankowski, Radomski, Niedzielan, Klos.
Wales: Coyne, Edwards, Gabbidon, Collins, Partridge, Ricketts, S Davies, Koumas, Fletcher, Giggs, Earnshaw. Subs: Price, Roberts, Page, Duffy, Craig Davies, Ledley, Robinson.