The match saw Anthony Martial make his first appearance for Sevilla since joining on loan from Manchester United in the January window. Martial started and played for 77 minutes before being withdrawn for Munir El Haddadi.
The visitors had a golden opportunity to score the winner in the dying seconds of the match with a penalty earned for a foul on Jules Kounde, given by the video assistant referee, but goalkeeper Sergio Herrera saved Ivan Rakitic's spot kick.
"There is nothing better than stopping a penalty in stoppage time," Herrera told reporters. "Our team was outstanding in defence against one of the best teams in the country, so we need to be happy that we made our fans proud."
Osasuna dominated possession and had the best of the few opportunities that were created in a lacklustre game in Pamplona.
Eight minutes later, Chimy Avila had another chance for the hosts but blasted his effort from just outside the box high over the bar.
Avila and Moncayola also had opportunities in the second half as Sevilla only had one chance through Jesus Corona, who dribbled past two defenders and into the area but missed the target with his shot.