Munoz scored in the 76th minute in Guadalajara on Tuesday night (Wednesday AEST) after the Colombians had been held back by a strong performance from Congo goalkeeper Lionel Mpasi, who made five difficult saves in the first 20 minutes.
Mpasi had no chance to stop Munoz's left-footed strike from inside the area after the ball deflected off a defender.
Congo twice came close to equalising in stoppage time, with Colombia goalkeeper Camilo Vargas making a superb save off a long-range strike by Nathanael Mbuku, then stopping a header by Chancel Mbemba off the ensuing corner kick.
Star Colombia forward Luis DÃaz had two goals called back in quick succession late in the second half, one for a foul in the 79th minute and another for offside in the 80th.
Congo had opened their first World Cup in 52 years with a surprising 1-1 draw against Cristiano Ronaldo and Portugal.
Colombia now have six points from two matches in Group K, two ahead of Portugal and five clear of Congo.
Portugal routed Uzbekistan 5-0 behind a pair of goals by Ronaldo earlier on Tuesday in Houston.
The Colombians need a draw against Portugal on Saturday to win the group. That result would also be enough to send Portugal to the knockout stage.
Colombia, who did not qualify for the 2022 World Cup, are ranked 11th in the world, third best among South American teams behind Brazil and Argentina.
Los Cafeteros opened with a 3-1 win over Uzbekistan.
Congo, ranked 47th, had their World Cup preparations affected because of an ebola outbreak. Many Congo fans were prevented from travelling for the tournament because of restrictions tied to ebola.
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