The Pamplona-based side had found themselves slipping perilously close to the relegation zone but victories over Espanyol and Real Betis in their last two matches, combined with previous draws against Real Madrid and Celta Vigo, had eased their concerns.
And they picked up another valuable point at ninth-placed Granada in a match the home side largely controlled - especially in the first half - but could not find a goal.
The closest either side came to making the breakthrough was in the 19th minute when Granada midfielder Recio hit the post from close range, while Osasuna keeper Asier Riesgo was the busier of the two custodians.
After Recio had seen his header from Fran Rico's corner come back off the woodwork, Riesgo was called upon to keep out efforts from Rico, Youssef El Arabi and Brayan Angulo either side of half-time and then again from Recio late on.
As well as those efforts, Granada also tried their luck through Jeison Murillo, Recio, Piti and El Arabi without managing to find the target.
Osasuna had few opportunities of their own, with the best being an early effort from Oriol Riera that just went wide, but they will feel it is a point gained from their trip to Los Carmenes against a Granada side who won their last home match 4-0 against Real Valladolid.