The visitors took the lead after 28 minutes when Pape Diakhate's error allowed Raul Garcia to score his first goal since returning to the club with a simple side-footed finish into an empty net.
Granada struggled to create chances throughout the 90 minutes but were handed a lifeline when poor defending by Osasuna allowed Rico acres of space just inside the area and he crashed home Ikechukwu Uche's cross with 25 minutes remaining.
Granada picked up their first win of the season with an excellent performance against Villarreal at Los Carmenes last weekend, but they failed to his those hits against an organised but limited Osasuna.
The hosts began the better and Andres Fernandez had to get down well to block Dani Benitez's low shot.
Moments later Osasuna had their first effort on goal, but Kike Sola's left-footed shot was too close to Roberto who made a comfortable save.
Osasuna then took the lead when Diakhate took a wild swing at Roland Lamah's cross but made no contact with the ball. The best Roberto could do was palm the ball back into the centre of the penalty area where Garcia was loitering and he was left with the simplest of finishes as he rolled the ball into the empty net.
Granada were then forced into two quick changes as Guilherme Siqueria and Carlos Martins went off injured and the limited flow that the game did have was all but destroyed.
Osasuna controlled the game better in the second half and Garcia saw another effort fly just over, before Benitez should have done better when the ball dropped to him on the left-side of the area but he smashed his shot well wide.
The hosts got their equaliser when Uche retrieved an overhit cross on the right and chipped a perfectly weighted ball back in to the area for the late-arriving Rico to volley first time past Fernandez.
Neither side went all out for a winner in the final 20 minutes but Osasuna were left aggrieved when in stoppage time substitute Ibrahima Balde had a goal wrongly ruled out for offside.