That gave Colombia the initiative to take the game to their illustrious opponents and they doubled their advantage three minutes into the second half.
Teofilo Gutierrez latched on to a through ball from James Rodriguez to shoot past Uruguay goalkeeper Fernando Mulsera to make it 2-0.
Gutierrez added his second goal of the match at the Metropolitano stadium in Barranquilla in the 52nd minute when he turned in Rodriguez's cross from close range.
Zuniga completed the comprehensive 4-0 victory for Colombia in the first minute of injury time.
The result leaves Colombia fifth in the CONMEBOL standings with 10 points from six matches, just one point behind Uruguay in fourth.