The South American side dictated play throughout the contest at Arrowhead Stadium, creating plenty of chances and registering eight shots on target.
However, Jhon Arias’ first-half strike was the only goal they managed despite their dominance.
The victory sends Colombia into the knockout stage, where they will face Switzerland in Vancouver on Tuesday for a place in the quarter-finals.
Ghana started brightly, with Thomas Partey sending an effort narrowly wide inside the opening minute, but that early attempt proved to be their only real threat.
Colombia suffered an early setback when Jhon Cordoba picked up what appeared to be a groin injury and had to be replaced by Luis Suarez.
Shortly afterward, Ghana also made a forced substitution as Marvin Senaya was unable to continue, with Alidu Seidu taking his place.
The breakthrough came in the 14th minute when Suarez worked hard to keep possession on the right before delivering a cross into the box, where an unmarked Arias calmly guided the ball into the net.
The goal left Ghana, who had managed only two goals during the group stage, chasing the game against a confident Colombian side.
Backed by a lively crowd in Kansas City, Colombia continued to control possession and attack with pace and creativity as they searched for another goal before the break.
Luis Diaz came close to extending the lead in the 39th minute, but the Bayern Munich forward failed to connect cleanly with his shot, sending it wide.
Moments before halftime, Ghana goalkeeper Lawrence Ati Zigi produced an excellent save to deny Johan Mojica’s powerful header.
The first-half statistics highlighted Colombia’s superiority.
Ghana failed to register a single shot on target and completed fewer than half the number of passes their opponents managed, although the scoreline remained just 1-0.
Colombia continued to create opportunities after the restart but struggled to put the game beyond Ghana’s reach.
Diaz thought he had scored, only for the offside flag to rule out the effort. Soon after, he tested Zigi again, but the goalkeeper made a comfortable save.
Juan Quintero also went close late in the match, firing a powerful effort just wide of the post.
In the end, Arias’ early finish proved enough as Ghana ended the game without recording a shot on target.
Diaz, who was named Player of the Match, said Colombia’s performances were improving with every game, even though he acknowledged the team needed to be more clinical in front of goal.
“We’re just missing that little detail of finishing a bit better and staying composed. I think we played a very solid game,” he said.
The winger also admitted he was disappointed not to score after getting into promising positions.
He said, “I had chances to convert. That confidence I want to have isn’t quite at 100 per cent yet.
“I’m trying to improve game by game. I felt much better in today’s match than in the previous one, without a doubt.”
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