Any victory for England would have seen them top Group A - booking a last-four position in the process - and goals from Demarai Gray, Jacob Murphy and Lewis Baker saw the Three Lions progress from the group stage in Poland.
England boss Aidy Boothroyd made one change to the team that started the 2-1 win over Slovakia Under-21s, with Leicester City's Gray taking the place of Chelsea forward Tammy Abraham, who dropped to the bench.
As a result, John Swift kept his position in the XI at the expense of Murphy, while the centre-back pairing of Alfie Mawson and Calum Chambers meant that Rob Holding had to make do with a spot on the bench once again.
As for Poland, their team showed two changes to the one that drew with Sweden Under-21s last time out - Krzysztof Piatek and Radoslaw Murawski taking the places of Mariusz Stepinski and Pawel Dawidowicz. Leicester City's Bartosz Kapustka and Arsenal's Krystian Bielik, meanwhile, remained on the bench for the host nation.
England had three half-chances inside the opening five minutes, but James Ward-Prowse saw his dipping effort from a Swift corner tipped over by Jakub Wrabel, before Baker had a shot blocked, and Mawson headed a corner wide of the post.
Boothroyd's side were ahead in the sixth minute, however, when Gray collected a clever pass from Leicester teammate Ben Chilwell before finding the far corner of the net, albeit with the help of a deflection as Wrabel was left clawing at thin air.
Gray continued to cause the host nation problems with his pace and movement in the final third, and the attacker delivered a low cross into the Poland box in the 22nd minute, but Redmond failed to make contact after dropping into a different area.
England twice came close to doubling their lead 10 minutes before the end of the first period, but Chalobah and Mawson both saw their close-range headers kept out by Poland's impressive goalkeeper Wrabel.
Swift was the next player in a white shirt to attempt to beat Wrabel, but Poland's stopper made another diving save as the home side stayed in the match, and indeed the tournament, entering the second 45 minutes, despite a half of utter domination from the Three Lions.
England lost Chalobah and Redmond to injury in the first period, however, with Will Hughes and Murphy both coming off the bench for Boothroyd's side.
Swift had a super chance to double England's lead in the 55th minute when he met a far-post free kick from Ward-Prowse, but the midfielder's effort flew wide of the post as Poland survived once again.
Murawski then had a decent chance to level the scores 25 minutes from time after Pickford's loose pass found Poland's number eight, but his effort was deflected wide of the post, much to the relief of Everton's new goalkeeper.
England were always a threat on the counter-attack, however, and Boothroyd's side doubled their lead in the 69th minute when Murphy slid home from close range after Gray had put the ball on a plate for his fellow attacker.
Poland were almost back in the match in the 74th minute when Przemyslaw Frankowski looked to pick out the far corner with a low strike, but the ball just flew wide of Pickford's post.
Baker and Abraham both had opportunities to make it 3-0 England 10 minutes from time, but the former saw his powerful free kick beaten away, before the latter headed the rebound over the Polish crossbar.
England, who have joined Spain in the semi-finals, did score their third in the 82nd minute, however, when Baker found the back of the net from the penalty spot after Jan Bednarek brought Abraham to the ground, which led to the Polish defender picking up his second yellow card on a night to forget for the home side.
England's semi-final will take place on June 27, although their opponents are yet to be confirmed.