Colombia kept their World Cup dream alive – and the bad news for England is that the South Americans look like a team to be reckoned with.
Goals by Barcelona defender Yerry Mina and Premier League rejects Radamel Falcao and Juan Cuadrado sent Poland home.
It means Jose Pekerman's men head into their last game against Senegal on Thursday with their fate in their own hands.
And a potential last 16 showdown with Gareth Southgate's England is on the cards.
Senegal and Japan lead group H on four points apiece – while Poland can book their tickets home after losing their first two group games for the third successive World Cup they have qualified for.
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Colombia, beaten by Japan in their opening game after playing 87 minutes with 10 men, looked increasingly like the team who were quarter-finalists four years ago.
An estimated 30,000 Colombians have made the trip to Russia – and the yellow-shirted hordes who turned the Kazan Arena into a mini-Bogota will also be a factor.
Colombia had to wait until five minutes before half-time before getting the breakthrough, but once Mina opened the scoring it was game over.
Johan Mojica and Juan Quintero combined at a short corner to spring James Rodriguez and his delicious cross into the heart of Poland's six-yard box was gobbled up by the leaping Mina.
Poland, the nation of Deyna, Lato and Boniek, went out with a whimper.
Robert Lewandowski may have scored 16 goals in qualification but the Bayern Munich hit-man's only sniff of a goal came just before the hour when he broke clear only for Arsenal keeper David Ospina to race out to block.
Falcao wasted one great chance – blazing over from 18 yards – but the striker who couldn't make it at Manchester United or Chelsea didn't miss when Quintero sent him racing through the middle.
Falcao's classy finish, with the outside of his left foot, gave Wojciech Szczesny no chance.
Quadrado was another who failed to make the grade at Stamford Bridge.
But when Rodriguez's stunning switch of play caught Poland out, the winger showed great pace and perfect placement into the corner.
No wonder Colombian legends Rene Higuita and Carlos Valderrama danced in delight in the posh seats.
Poland (3-4-3): Szczesny 5; Piszczek 5, Bednarek 5, Pazdan 5; Bereszynski 5, Krychowiak 6, Goralski 6, Rybus 6; Zielinski 5, Lewandowski 5, Kownacki 5. Subs: Grosicki (Kownacki 57), Teodorczyk (Bereszynski 72), Glik 5 (Pazdan 80).
Colombia (4-2-3-1): Ospina 6; Arias 6, D Sanchez 6, Mina 7, Mojica 6; Aguilar 5, Barrios 6; Cuadrado 8, Quintero 7, Rodriguez 8; Falcao 7. Subs: Uribe 6 (Aguilar 32), Lerma 5 (Quintero 73), Bacca 5 (Falcao 78).