Busy Chile midfielder Rodrigo Valenzuela, who drew three yellow cards from Costa Rica players, attracted the first two in quick succession when he was fouled by Cristian Badilla and Leonardo Gonzalez. The second one led to the free kick from which Olarra scored.
Olarra was in the right place at the right time. Luis Jimenez's free kick glanced off the head of defender Badilla and in off Olarra's turning right shoulder.
It could have been 2-0 seven minutes after the break, but Jimenez's hard shot hit the underside of the crossbar and bounced out.
Pinto, appointed as Costa Rica coach only two weeks before the Copa, changed his lineup at halftime by fielding three forwards, in search of the win.
"I decided we had to go for it and the tactical change made all the difference," he said.
Costa Rica equalized just before the hour mark. Alonso Solis' free kick rebounded to teammate Walter Centeno, whose blast from the right might have gone in if it wasn't accidentally trapped in the goalmouth by the long legs of Wright, who had an easy tap-in.
The result was a double celebration for Costa Rica captain Luis Marin, who made his 100th international appearance.
Both invited guests from CONCACAF, Costa Rica and Mexico, made it to the last eight for a second consecutive Copa. In 2001, Costa Rica lost in the quarterfinals and Mexico went to the final.
Olmos said Chile's early exit was a worrying sign that the country's pool of quality players was dwindling. The elimination was "a smack in the face of our reality," he said. "It should serve as a wakeup call about our universe of players. An injury or a suspension has an immediate impact on our team."
Colombia and Peru will find that out this weekend, after the Copa disciplinary committee handed one-game bans to Colombia's Arley Dinas and Gonzalo Martinez, and Peru's Jefferson Farfan, for accumulating two yellow cards.
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