Colombia kept their hopes of reaching the World Cup knockout stages alive by ending Poland's chances with a 3-0 victory in Kazan.
The result means Poland will definitely be going home after their final Group H game with Senegal on Thursday, while the South Americans can still go through.
A victory will guarantee their progression and they are 4/6 with Sky Bet to qualify and 40/1 to win the competition.
The 2014 quarter-finalists had been in danger of elimination following an opening loss to Japan, but they produced a brilliant attacking display against the Poles.
They opened the scoring five minutes before the interval, with the attacking triumvirate of James Rodriguez, Juan Cuadrado and Juan Fernando Quintero all involved from a short corner. The former was allowed space to deliver a perfect cross from the right that Barcelona defender Yerry Mina just had to guide beyond an oncoming Wojciech Szczesny with his head.
Nobody scored more goals across Europe in qualifying than Poland's Robert Lewandowski, but the Bayern Munich man was being starved of service while their opponents appeared awash with creativity.
Poland's hopes of getting back into the contest were dashed 20 minutes from time when Falcao, who was ruled out of the 2014 tournament through injury, scored his country's second.
He was released by a terrific ball from Quintero, who weighted the pass perfectly to allow Falcao to take one touch and coolly slot an outside-of-the-foot finish into the net.
Colombia were not done there and their third goal may have been the pick of the bunch.
Rodriguez created it from the byline when he spotted Cuadrado in space down the middle. The ex-Chelsea winger took two touches to race through and then placed his effort beyond Juventus team-mate Szczesny and into the corner of the net.
GOAALLL! Yerry Mina heads Colombia ahead against Poland after a great cross from James Rodriguez.#WorldCup #COL #POLCOL pic.twitter.com/FGJn3TnG7f
— ITV Football (@itvfootball) June 24, 2018
GOAALLL!! Falcao doubles Colombia's lead with a fine low finish off the outside of his boot!#WorldCup #COL #POLCOL pic.twitter.com/jEFLDH3T9t
— ITV Football (@itvfootball) June 24, 2018
GOAALLL! Juan Cuadrado bursts free and finishes Colombia's third goal against Poland after a brilliant through pass from James Rodriguez.#WorldCup #COL #POLCOL pic.twitter.com/14M5BqmMln
— ITV Football (@itvfootball) June 24, 2018
Odds correct at 2100 BST on 24/06/18