Barcelona defender Yerry Mina headed home the winner from a corner kick to secure Colombia's passage to the knockout phase.
The referee had overturned his original decision to award a penalty to Senegal after consulting the video assistant referee system in the 17th minute.
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Colombia midfielder James Rodriguez, who top-scored at the 2014 FIFA World Cup in Brazil with six goals, was substituted soon after the half-hour mark with an apparent injury.
Previously, the Senegalese team bested Poland 2-1 and tied 2-2 with Japan, while their counterparts from Colombia crushed Poland 3-0 and lost to Japan 1-2.
The 2018 FIFA World Cup kicked off on June 14 and will continue until July 15, with the matches being played in 11 cities across Russia.