Colombia, focused throughout the Wednesday's match on circling Qatar's goal, scored their winner five minutes before the end, when James delivered a brilliant floating cross to Zapata's head and the Atalanta striker from Bergamo netted the sole goal of the game, reports Efe news.
The South American squad pressed from the start and dominated the first half of the match against Qatar, on the second match day of Group B, but the Asian Champion managed to go into the break with a blank scoreboard.
Roger Martinez had a goal ruled out for offside after just five minutes of play and Rodriguez sent an unpressured header wide just eight minutes later.
The score 0-0 of the first half gradually calmed the "yellow" euphoria of the Colombian fans, who were loudly cheering their team from the stands and gave way to the shouts of the small number of Qatar supporters present, who were joined by a few Brazil. Colombia jacked up the intensity for the second half with more pressure and speed.
At the beginning of the second half, in the 48th minute, a shot by Martinez hit the arm of Qatari defender Abdelkarim Hassan. The referee initially sanctioned as a penalty and yellow for Hassan, but after consulting the VAR, he annulled the previous decision.
Colombia's coach Carlos Queiroz, who had already replaced Medina with Atletico Madrid's Santiago Arias, sent his most experienced players Radamel Falcao Garcia and Luis Diaz on the field to add pressure in the attack, but Qatar still resisted the Colombian onslaught.
Colombia kept looking to score after the goal and Mateus Uribe and Zapata again had chances in front of Saad Alsheeb's net. Colombia proved their greater experience with 69 per cent of ball possession against Qatar's 39 per cent. They also had five shots on target and 13 corners against two and one, respectively, for the As.
The win leaves Colombia at the top of Group B with six points, after their 2-0 win over Argentina in their first match on Saturday.
Qatar, meanwhile, have one point after a 2-2 draw against Paraguay in their Copa America debut in Rio de Janeiro on Sunday.
( With inputs from IANS )