The Europeans tried to fight their way back and threw players forward in the final 15 minutes, but they were unable to find any consolation as the match ended 3-0 in favour of the Colombians.
That proved to be final piece of goal-mouth action in the second stanza as the Colombians register their first win, while Poland have been eliminated.
With two losses after two games, Poland has zero points. None of Poland's nine World Cup games against South American opponents has finished as a draw, with the Eagles winning four and losing five.
Lewandowski's side were crushed by Colombia over the 90 minutes and Rodriguez set up two of their goals with two superb crosses.
"They were seen as one of the favourite teams coming into the World Cup, so I'm expecting a very hard match, a very intense match".
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"We're going to play creative football and I'm certain we will do enough to win this game", he said.
Falcao then broke through in the second half before driving a low strike into the far corner and Juan Cuadrado capped off a fine team performance with an accomplished finish after racing on to James' sublime ball behind the Poland defence.
Bayern Munich star James then found Juan Cuadrado late on, wrapping up a comfortable win for Colombia and leaving Nawalka with hard questions to answer.
"I'm very sorry and very sad about the result, but tomorrow's another day and we have to come to terms with things", said Poland coach Adam Nawalka.
The 22-year-old enjoyed his first taste of World Cup action on Monday as he impressed after coming on as an 80th minute substitute in the 2-1 victory over Tunisia.
Poland threatened again, but when Lewandowski got his head to a cross into the area he was marked by both Mina and Davinson Sanchez. Cuadrado collected the pass and rushed toward the box, timing his shot perfectly to beat goalkeeper Wojciech Szczesny.