Poland started the second half a much better side and nearly levelled matters on the hour mark when Robert Lewandowski showed great skill inside the box to bring a lofted cross under control before seeing his shot from 14 yards well-stopped by the Colombian keeper.
Quintero's defence-splitting pass then gave captain Falcao, who missed the 2014 tournament due to injury, his first World Cup goal in the 70th, while Rodriguez got his second assist five minutes later when he set up Cuadrado to make it 3-0. Adam Nawalka's men were completely outplayed on the night by a determined Colombian side who finally kick-started their campaign with a thumping win, after losing to Japan in their opening game.
"Maybe that's all we could do. Let's be frank, it's not like we lost by a whisker", said Lewandowski.
"But we're not going to go insane, mentally we're in a good place but we need to continue to improve because we are ambitious and we want to continue in this World Cup as we hoped".
"I'm very sorry and very sad about the result, but tomorrow's another day and we have to come to terms with things", he said.
Poland led their qualifying group nearly from start to finish, finishing with eight wins, one draw and a defeat with Lewandowski leading Europe's qualifying campaign with 16 of the side's 28 goals.
It means that in the last two tournaments, no player has been involved in more goals than James.
With the Eagles on the ropes, Colombia sought to confirm three points as they pressed for a second and it arrived with 20 minutes left to play.
"Colombia are an excellent team with an excellent coach".
The respite was brief and on the next Colombia attack Juan Quintero found Rodriguez inside the box and he chipped the ball into the danger area for Mina to head into the net from point-blank range.
Another devastating move handed Colombia their third goal in the 75th minute.
"We're going to play creative football and I'm certain we will do enough to win this game", he said. "It was clear there was more and more free space for the Colombian team, and they really put it to good use and that's why they won".