Yerry Mina (40th minute), Radamel Falcao (70th) and Juan Cuadrado (75th) scored for Columbia.
The win kept alive Columbia’s chances of advancing from the group stage.
They are on three points from two matches. They had been defeated 1-2 by Japan in their first game.
Poland, who had been defeated by Senegal in their previous match, have no points and are as good as out of the tournament.
Colombia dominated proceedings right from the start.
The South Americans controlled possession beautifully and Poland struggled to contain their star-studded attacking line-up.
Cuadrado was impressive form, keeping the capacity crowd awestruck with his runs down the right wing.
He formed a superb combination with Juan Quintero and the duo created all sorts of problems for the Poland defense.
Apart from his good work upfront, Cuadrado also did some really good defensive work, falling back with speed whenever Poland went on the counter.
Poland never really seemed to be in the game and created very little scoring chances.
They have one of the best centre-forwards in the world in Robert Lewandowski but Poland’s link up play from the midfield was rendered ineffective by Columbia’s excellent defensive organization.
The Bayern Munich star was left totally isolated in the absence of proper support from the midfield.
Whenever Poland went on the attack, Colombia’s speed down the flanks saw the Europeans being caught on the counter.
Colombia took the lead shortly before halftime off a corner when James Rodr Aguez floated in a cross into the penalty box and Mina rose above the Poland defence to head the ball in.
The South Americans continued to dominate after the break and created scoring chances at regular intervals.
But a combination of poor finishing and excellent defending by Poland prevented them from scoring.
But Colombia could not be denied for long as Falcao, who seemed to be struggling with his form, finally found his scoring touch.
A quick attack by Colombia saw Quintero put forward an excellent through and Falcao raced into the opposition box and calmly slotted home into the bottom-left corner.
Poland were forced to go all out in attack which saw Cuadrado score Colombia’s third goal off a fast counter a short while later.
James initiated the move charging out of defence down the left wing before finding Cuadrado upfront.
Cuadrado, who had raced down the right wing before receiving the ball in the centre, continued his run and beat Poland goalkeeper Wojciech Szczesny with an excellent finish.
That virtually sealed the issue as Poland never seemed capable of scoring and Colombia clinched a well deserved victory.