Barcelona defender Yerry Mina scored the opening goal in the 40th minute as he powered a header beyond Wojciech Szczesny.
This was followed by Falcao's first World Cup goal that came in the 70th minute of the game.
The presence of James Rodriguez - fully fit again after a calf injury - vastly improved Colombia's link-up play following a below-par performance in their 2-1 defeat to Japan in the opening game.
In the 75th minute, Rodriguez provided a smooth assist to Cuadrado to add a third goal that put the game well beyond Poland's reach.
The win kept alive Columbia's chances of advancing from the group stage. They are on three points from two matches.
Poland, who had been defeated by Senegal in their previous match, have no points and are now out of the tournament.
The South Americans controlled possession beautifully as Poland struggled to contain their star-studded attacking line-up.
Poland never really seemed to be in the game and created very little scoring chances.
Columbia will next take on Senegal on June 28, while Poland will play against Japan on the same date.