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.
Pekerman is expected to alter his setup a little against Senegal, with Sevilla forward Luis Muriel thought to be in line to partner with Radamel Falcao in attack after the Monaco star cut a frustrated figure last time out.
In contrast, this was another disappointing display by Poland, who lost to Senegal in their group opener.
Midfielder James Rodriguez, victor of the Golden Boot at the last World Cup, returned to the starting lineup after injury and played a part in two of the goals as Colombia got back on track after their opening loss to Japan.
And a potential last 16 showdown with Gareth Southgate's England is on the cards.
Poland can not now catch either Japan or Senegal, who have four points from two games. Subscribe to our SMS sports service by texting "SPORTS" to 22840.
Rodriguez's short corner eventually found Quintero, whose smart through ball back to Rodriguez gave him time and space to curl a flawless left-footed cross that Mina rose to header powerfully past Szczesny on 40 minutes.
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.
Poland, the nation of Deyna, Lato and Boniek, went out with a whimper.
It was Los Cafeteros who enjoyed the first real chance.
The match started to a barrage of noise from the yellow-shirted Colombian fans and the early exchanges were frenetic with Poland putting in some physical challenges and Robert Lewandowski getting close attention from the Colombian defence.
Falcao's classy finish, with the outside of his left foot, gave Wojciech Szczesny no chance.
Poland played well for 15 minutes but then faded.
No wonder Colombian legends Rene Higuita and Carlos Valderrama danced in delight in the posh seats. With plenty of work still do, the Juventus winger out-sprinted Michal Pazdan and Rybus before stroking the ball beyond Szczesny.
Starting alongside Juan Quintero and Cuadrado on the right, Colombia's ultra-offensive starting line-up was a forewarning. Subs: Uribe 6 (Aguilar 32), Lerma 5 (Quintero 73), Bacca 5 (Falcao 78).