Colombia top their group with six points after two matches, ahead of Costa Rica and Brazil, who have one point each. Paraguay are bottom with zero points and face Brazil later on Friday.
'Los Cafeteros', who will finish the evening first in the group regardless of the later result, sealed a tenth consecutive victory and 25th match without defeat as they pursue their first Copa America title since 2001.
A draw between Brazil and Paraguay could see Nestor Lorenzo's squad secure their top spot in the group, thus avoiding a probable quarter-final against Uruguay.
If not, a draw in their final group match against Brazil on Tuesday should suffice.
Despite the loss, Costa Rica, who have one point, are still in the running, but they need to secure a win in their final match against Paraguay and hope for other results to go their way.
Colombia started the match well and took the lead in the 31st minute through Liverpool winger Diaz, who confidently converted from the penalty spot after Costa Rica goalkeeper Patrick Sequeira bundled over Cordoba in the box.
As Costa Rica pressed for an equaliser they left themselves open on the break and Colombia made them pay, with Sanchez outmuscling defender Juan Pablo Vargas to head Jhon Arias' corner past Sequeira from close range in the 59th minute.
After scoring, Sanchez held up the jersey of team mate Jhon Lucumi, who missed the match due to an injury.
Cordoba rounded out the scoring three minutes later after timing his run perfectly to stay onside and latch onto James Rodriguez's long ball before calmly slotting his finish past Sequeira.
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