Neither nation produced a scintillating attacking display in normal time or extra time - barring a disallowed Ben Davies goal towards the end of the first half - but a nail-biting shootout began with nine perfect penalties before Daniel James stepped up to the spot.
However, needing to score to force sudden death, the Leeds United winger's spot kick was beaten away by Wojciech Szczesny, as Michal Probierz's men punched their ticket to Germany and left Rob Page's men heartbroken.
Despite finding the back of the net in the Dragons' semi-final success over Finland, David Brooks was demoted to the bench by Page, who instead brought on Kieffer Moore as the focal point of his attack.
The Ipswich Town hotshot and Robert Lewandowski cut isolated figures in the opening exchanges, though, as neither team went for the jugular early doors, barring an 11th-minute Karol Swiderski effort which just crept past the post.
Szczesny was given something to think about in the 17th minute, but Davies's header from Harry Wilson's corner also missed the target, and the game was still waiting for its first shot on target as the half-hour mark approached.
As an incredibly cagey opening period drew to a close, though, Davies ostensibly thought that he had headed home the opener for the hosts, only to be correctly denied by an offside decision after meeting Moore's knock-on.
While elation quickly turned to despair, Wales ought to have been encouraged by that near-miss right at the end of the half, and true enough, the hosts were in the ascendancy straight after the restart.
Szczesny was forced into a terrific fingertip stop from Moore's 48th-minute header, but both teams were still struggling to hit top gear in Cardiff, despite the best efforts of the fervent fans.
As Poland began to threaten again, Page made the bold decision to withdraw Tottenham Hotspur's Brennan Johnson for James, while Connor Roberts went down injured in the dying embers and was taken off for Brooks.
The tie remained on a knife-edge as injury time loomed, and the extra 30 minutes that seemed inevitable did arrive after a goalless 90, where the visitors could not muster a single attempt on target but did not come under major duress defensively.
Jakub Piotrowski almost changed that for the Eagles in the 99th minute, cutting inside and letting fly with a swerving right-footed strike from outside the box, but his stunning effort was just a fraction too high and wide.
As penalties entered the minds of both managers, Page sacrificed the unfortunate Brooks - who had only been on the pitch for half an hour - for Nathan Broadhead; whether the former had picked up a knock or was regarded as an inferior spot-kick taker was anybody's guess at the time.
Wales finished the 120 minutes with 10 men as Chris Mepham picked up a second yellow card, but the defender's sending-off was incredibly inconsequential, as both beleaguered sides entered their pre-penalty huddles.
Lewandowski, Sebastian Szymanski, Przemyslaw Frankowski, Nicola Zalewski and Krzysztof Piatek all found the mark from 12 yards for Poland, as did Davies, Moore - just - Wilson and Neco Williams for the Welsh.
The dreaded fifth penalty responsibility fell on the shoulders of James, but Szczesny guessed correctly and sprung to his right to deny the ex-Manchester United man, and Poland immediately surged down to the other end of the pitch to celebrate with the travelling crowd.
A place in a daunting Group D with France, the Netherlands and Austria awaits Poland, who have qualified for their fifth successive Euros, while Wales miss out on a third successive appearance at the continental competition.