Goals from Yerry Mina, Radamel Falcao and Juan Cuadrado capped off a destructive showing from Jose Pekerman's side, whose victory also means that Poland find themselves eliminated from the tournament with a game still to be played.
Aiming to bounce back from a listless defeat to Senegal, Poland's switch to a 3-4-3 initially appeared to re-energise the Eagles, as an early ball into Robert Lewandowski required some strong defending from both Davinson Sanchez and Mina to thwart the frontman.
Colombia had plenty of work to do themselves after going down to Japan, and after a watchful opening Los Cafeteros soon began to apply themselves going forward. Cuadrado crossed adroitly into the middle, before Jan Bednarek intervened to deny some cunning movement from Falcao.
Poland began to fade as the first half wore on and some standout play from Juan Fernando Quintero and Cuadrado set Santiago Arias away into space on the right, but the full-back saw his cross turned away by Michal Pazdan at the near post.
Cuadrado proved a standout performer in the opening 45 minutes and he showed sublime skill to trick his way past two men and find the byline, although his delivery was eventually cleared despite causing chaos inside the Poland box.
Adam Nawalka's charges drifted worryingly heading towards the interval and Colombia made them pay on the 40-minute mark having caught the Eagles cold at a corner, much to the chagrin of their animated coach on the touchline.
The set piece was sent short to Quintero, who found James Rodriguez down the right side of the box, and he produced a skilfully chipped ball towards the back post. Centre-back Mina rose to the challenge as he climbed highest to power a header beyond a helpless Wojciech Szczesny in the Poland goal.
Colombia started the second half just as impressively and an adroit counter-attack soon saw James release Quintero, but the playmaker saw his driven effort deflected away before it could test Szczesny.
Poland continued to struggle creating chances and their best of the half came from a route-one ball out from the defence that saw Lewandowski break free of Mina, although David Ospina was quick off his line to make a crucial save down low.
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. Quintero proved the architect with a sublime through-ball, allowing Falcao to break free and prod a clever finish into the bottom corner.
Colombia proved rampant in the closing stages and Pekerman's charges perhaps saved their best goal for last. James pulled away on the right inside his own half, before curling a ball across the Poland backline to set Cuadrado free and he made no mistake by curling an unerring finish beyond Szczesny.
Victory for Los Cafeteros now leaves the South Americans with more than an outside chance of reaching the knockouts. Beating Senegal in the nation's final group game would guarantee Colombia safe passage into the second round, while Poland's fate has already been sealed after just two disappointing group games.
POLAND (3-4-3): Szczesny; Pazdan (Glik 80'), Bednarek, Piszczek; Krychowiak, Goralski, Rybus, Bereszynski (Teodorczyk 72'); Zielinski, Kownacki (Grosicki 57'), Lewandowski
COLOMBIA (4-2-3-1): Ospina; Arias, Y. Mina, Sanchez, Mojica; Barrios, Aguilar (Uribe 32'); Quintero (Lerma 73'), James, Cuadrado; Falcao (Bacca 78')