Colombia 0-0 Uruguay (4-2 pens): Ospina sends Cafeteros into Copa semi-finals
After both sides went scoreless in normal time, Los Cafeteros converted on all four of their penalties while veteran Ospina saved attempts from Jose Gimenez and Matias Vina.
That left Colombia to celebrate their triumph in a hard-fought, physical encounter in Brasilia after Los Cafeteros had struggled into the quarter-finals.
Uruguay entered the quarter-finals having won two games in a row, while Colombia had been defeated in their final two group-stage games.
After waiting 10 days since their last game, Colombia looked the more energetic side in the opening half, out-shooting Uruguay 4-1 but Fernando Muslera had little to do in the Uruguay net.
Luis Muriel fired wide on an open look just prior to half-time, minutes after sending a free kick from a dangerous spot over.
Colombia's momentum carried over to the second half, as Luis Diaz drove straight to the Uruguay goal in the opening seconds but could not get a clear look.
Uruguay's first dangerous chance came in the 50th minute, when Nahitan Nandez curled a ball in from the right side that caught Ospina off-balance, but the goalkeeper acrobatically tipped the ball away from the top corner.
Colombia came close in the 73rd minute as Rafael Borre's cross from the right side found Duvan Zapata, but Muslera parried away the header from eight yards.
Both sides charged forward at every opportunity in the final 15 minutes but neither came close to scoring as Colombia kept Luis Suarez and Edinson Cavani at bay throughout.
It was the fourth consecutive Copa America quarter-final for Colombia in which the game was scoreless in regulation.