Demarai Gray opened the scoring early on with a long-range effort before substitute Jacob Murphy tapped in.
Poland rarely threatened and had defender Jan Bednarek sent off late on for tripping Tammy Abraham in the box.
Lewis Baker converted the resultant penalty to complete the win.
The victory against the hosts means Aidy Boothroyd's side top the standings with seven points.
Relive England's win against Poland
England can now look forward to a semi-final at the Stadion Miejski in Tychy on Tuesday, 27 June [17:00 BST] although they will not know who they will face until the completion of the group stage on Saturday.
They will play either Portugal from Group B or Germany, Italy or the Czech Republic from Group C.
There are only three groups at the tournament - with the three winners each progressing along with the best-placed runners up.  Who England play depends on who claims the spot as the best runner-up.
At the moment Slovakia, who finished second in Group A behind England with six points and a goal difference of +3, are in a strong position to claim it.
If that happens then England will play the winner of Group C, which with one round of games left to play is topped by Germany with six points.
However, if Slovakia do not claim that place then England's last-four opponents will be either Portugal (who are the only team in Group B that could finish in a better position than Slovakia) or Germany, Italy or the Czech Republic (who could all finish in second place with a better record than Slovakia) in Group C.
England's first 135 minutes of football at the tournament did nothing to suggest they were capable of avoiding a third successive group-stage exit.
They were unadventurous and ponderous in the opener against Sweden, managing just a single shot on target, and were equally poor for the first 45 minutes of their second game against Slovakia, in which they trailed 1-0 at the break.
However, they showed grit and determination to fight back and win that game 2-1, putting them in control of their own destiny, and they came out fighting in an intimidating atmosphere against Poland.
Goalkeeper Jordan Pickford once again showed why Everton paid Sunderland £30m for his services with a confident and assured display, while the Leicester pair of Ben Chilwell and Gray were also excellent.
Chilwell dominated down the left, snubbing out Poland attacks while getting forward quickly to create chances, and it was from his excellent pass that Gray scored the opener.
But in truth there were standout performances all over the pitch for England.
Southampton midfielder James Ward-Prowse provided a threat from set-pieces that is so often lacking at senior level, while Alfie Mawson was a dominant presence in defence as well as offering an aerial threat in attack.
The Swansea defender was only denied adding his name to the scoresheet by an excellent Jakub Wrabel save.
After a slow start it appears England are finding their form just at the right time.
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It has been a good summer of major tournament football so far for England.
They reached the final of the European Under-17 Championship before losing to Spain on penalties.#
England then claimed their biggest international title since 1966 when their Under-20 side won the World Cup earlier this month, and now the Under-21s are now just two wins away from lifting another major trophy.
However, Spain have been the standout team at the tournament so far. They were the only team to secure their place in the semi-finals with a game to spare and boast some outstanding talent.
Saul Niguez, an Atletico Madrid regular and capped three times by the Spanish senior side, scored a memorable overhead kick in a 5-0 defeat of Macedonia, with Real Madrid's Marco Asensio scoring a hat-trick in that game.
Germany have also won their two games so far and have the tournament's most formidable defence - they are the only team yet to concede a goal.
However, if England perform like they did against Poland then they have every chance of emulating their Under-20 counterparts.
England Under-20 boss Paul Simpson, who was co-commentator on the game for BBC Radio 5 live:
"That was a top, top performance from the first whistle. They did everything manager Aidy Boothroyd would have wanted. It wasn't done by lumping it forwards, it was controlled possession while also being a real threat from set-pieces.
"This performance puts a marker down and shows what we are all about - we are not just here to make up the numbers, we are into the semi-final. And we can go on and get even stronger."
England Under-21s boss Aidy Boothroyd: "It's a great moment. After the first game, which was a draw, it was doom and gloom. But we have a good group here and got the two wins that we needed. It was a high-pressure game, if we hadn't won then we would be out.
"We carried out the game plan to a T. We controlled the game and played really well. There were a few nervy moments.
"Demarai Gray was terrific. He worked his socks off. It is a squad game and one of the hardest things is keeping the lads who aren't playing motivated. But it is a good group, I'm really pleased."
Match ends, England U21 3, Poland U21 0.
Second Half ends, England U21 3, Poland U21 0.
Corner,  Poland U21. Conceded by Alfie Mawson.
Attempt missed. Przemyslaw Frankowski (Poland U21) left footed shot from outside the box misses to the left. Assisted by Patryk Lipski with a headed pass.
Ben Chilwell (England U21) wins a free kick in the defensive half.
Foul by Mariusz Stepinski (Poland U21).
Will Hughes (England U21) wins a free kick in the defensive half.
Foul by Patryk Lipski (Poland U21).
John Swift (England U21) wins a free kick in the attacking half.
Foul by Mariusz Stepinski (Poland U21).
Goal!  England U21 3, Poland U21 0. Lewis Baker (England U21) converts the penalty with a right footed shot to the bottom left corner.
Second yellow card to Jan Bednarek (Poland U21) for a bad foul.
Penalty England U21. Tammy Abraham draws a foul in the penalty area.
Penalty conceded by Jan Bednarek (Poland U21) after a foul in the penalty area.
Tammy Abraham (England U21) wins a free kick on the right wing.
Foul by Pawel Jaroszynski (Poland U21).
Attempt missed. Tammy Abraham (England U21) header from the centre of the box is high and wide to the left following a set piece situation.
Attempt saved. Lewis Baker (England U21) left footed shot from outside the box is saved in the bottom left corner.
Jan Bednarek (Poland U21) is shown the yellow card.
Tammy Abraham (England U21) wins a free kick in the attacking half.
Foul by Jaroslaw Jach (Poland U21).
Will Hughes (England U21) wins a free kick in the defensive half.
Foul by Karol Linetty (Poland U21).
Attempt missed. Przemyslaw Frankowski (Poland U21) right footed shot from the right side of the box is close, but misses to the left. Assisted by Mariusz Stepinski.
Foul by Will Hughes (England U21).
Patryk Lipski (Poland U21) wins a free kick in the defensive half.
Substitution, Poland U21. Mariusz Stepinski replaces Dawid Kownacki because of an injury.
Substitution, England U21. Tammy Abraham replaces James Ward-Prowse.
Attempt missed. Karol Linetty (Poland U21) right footed shot from outside the box misses to the left. Assisted by Patryk Lipski.
Goal!  England U21 2, Poland U21 0. Jacob Murphy (England U21) right footed shot from very close range to the centre of the goal. Assisted by Demarai Gray following a fast break.
Attempt blocked. Pawel Jaroszynski (Poland U21) left footed shot from outside the box is blocked. Assisted by Karol Linetty.
Delay over. They are ready to continue.
Delay in match Dawid Kownacki (Poland U21) because of an injury.
Corner,  Poland U21. Conceded by James Ward-Prowse.
Attempt blocked. Radoslaw Murawski (Poland U21) right footed shot from outside the box is blocked.
Alfie Mawson (England U21) is shown the yellow card for a bad foul.
Foul by Alfie Mawson (England U21).
Jaroslaw Niezgoda (Poland U21) wins a free kick on the right wing.
Substitution, Poland U21. Jaroslaw Niezgoda replaces Krzysztof Piatek.
Ben Chilwell (England U21) wins a free kick in the defensive half.
England reached the semi-finals of the European Under-21 Championship for the first time since 2009 after comfortably beating 10-man Poland to finish top of Group A.