With qualification already secured, Pekerman rested his stars as he made 10 changes to the starting line-up that beat Paraguay with midfielder Sebastian Perez the only player remaining, but he came to rue such extensive changes.
Costa Rica, having already been eliminated following the United States’ 1-0 win over the Paraguayans earlier on Saturday, had Arsenal’s Joel Campbell named among the substitutes with Sporting CP’s Bryan Ruiz chosen to lead the line.
Venegas opened the scoring with a superb strike from 20 yards after brilliantly bringing down a cross-field pass from Borges, beating the offside trap and bearing down on goal.
His progress was hindered by the Colombia defence, who forced Venegas to put his foot on the ball and turn out, but that did not stop him from scoring as he knocked the ball a yard ahead of him and dispatched a brilliant finish from distance that found the far top corner.
However, their advantage did not last long as Fabra embarked on a mazy run starting on the left wing and finishing with a trail of Costa Rica defenders in his wake before slotting the ball under Patrick Pemberton.
He followed the sublime with the calamitous when his disastrous own goal put Costa Rica back into the lead when he bundled Venegas’ cross into his own net at the far post.
Pekerman turned to James Rodriguez at half-time as he hoped to wrestle back control of the game and avoid a defeat that could yet see them facing off against Brazil in the quarter-finals.
But his gamble did not pay off as Borges made it 3-1 just before the hour-mark when he finished off a lovely overlapping run and cross from substitute Bryan Oviedo.
Substitute Juan Cuadrado set up Moreno for Colombia’s second as they chased a crucial equaliser but they could not find it as Pekerman was left to rue his selection.