Osasuna cut the gap to the top four in Spain to three points on Monday, sitting in seventh and 11 behind league leaders Barcelona. Sevilla are four points behind the Pamplona-based club in 11th.
The match struggled to spark into life at Ramon Sanchez Pizjuan Stadium in Seville but Budimir broke the deadlock in the 69th minute when he headed in a cross from Jesus Areso.
It was the Croatian international's ninth goal in his past 10 league matches.
Budimir is back in the goals. ⚽️— LALIGA English (@LaLigaEN) #SevillaFCOsasuna pic.twitter.com/f5SgMMDZ3tDecember 2, 2024
However, the visitor's lead lasted just three minutes. Dodi Lukebakio latched onto a ball over the top from substitute Saul and rounded goalkeeper Sergio Herrera to fire in the equaliser for the Andalusians.
Herrera and Sevilla counterpart Alvaro Fernandez pulled off crucial saves in the dying seconds to ensure their sides held on for a point in the final match of round 15.
"It's a point that we need to value as it was achieved away from home against a very good team," Budimir told Movistar.
"We did what we needed to do. Against Villarreal (2-2), we left with a bittersweet taste; today was similar as they equalised right after we scored. I would have liked to know what would have happened if we had held on for five more minutes with the score at 0-1.
"We would have liked the game to have been like the last 20 minutes throughout, but we leave with an important point."