Colombia has two convincing wins in its two games and even with one group game to go, it is guaranteed of finishing either in the top two in Group A or being among the best of the third-place teams.
Jose Valencia scored for Colombia in the 23rd minute and James Rodriguez added another in the 90th, giving the South Americans six points in two matches following a 4-1 opening game victory over France.
"I'm happy not only for the goal but because I helped the team reach our first goal which was to advance to the next round," Colombia's James Rodriguez said. "Mali was a tough opponent, but we played at a high level and that was important."
The last set of games in Group A will be on Friday when Colombia takes on South Korea at Bogota and Mali faces France in Cali. Colombia has six points, France and South Korea have three and Mali zero.
The top two teams in each of the six groups advance to the knockout stage and are joined by the top four third-place teams.
Earlier Tuesday, France beat South Korea 3-1 in Bogota on late goals by Gueida Fofana and Alexandre Lacazette.
Fofana scored in the 81st to break a 1-1 tie and Lacazette closed out the scoring in stoppage time. Gilles Sunu had given France the lead in the 27th before Kim Young-uk equalized in the 59th with a free kick.
"After the first match we really felt down," Lacazette said, referring to the Colombia loss. "But our friends and family told us to forget it and look forward to the next match."
In Group B, striker Nelson Oliveira scored in the 19th minute to give Portugal a 1-0 victory over Cameroon.
Portugal has four points, two more than Uruguay and New Zealand. Cameroon is last in the group with one point, but retains a chance to advance to the next round.
Cameroon played a man down from the 71st after defender Ghislain Mvom was red carded.
Earlier, Uruguay outplayed New Zealand from the start but was held 1-1.
Andrew Bevin took advantage of one of New Zealand's only chances to score with a header in the 57th, but Adrian Nicolas Luna equalized for the Uruguayans in the 74th with a right-footed shot into the far corner after a well-crafted attack.
Uruguay had 58 percent of the possession and outshot New Zealand 25-8 at the Pascual Guerrero stadium, but New Zealand goalkeeper Stefan Marinovic made several key saves.
"We deserved better luck," Uruguay coach Juan Verzeri said. "Their goalkeeper stopped everything."
Uruguay will finish group play against Cameroon, while New Zealand will face Portugal.
"I'm satisfied with the team's performance, but not with the result," New Zealand coach Chris Milich said. "We earned our first points in the World Cup but we didn't come here to draw matches, we want to win them."
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