The stalemate, which lacked clear scoring chances until the final minutes on Friday, left Osasuna in ninth place and Mallorca in 11th.
Defender Jose Copete was shown a straight red card in the 69th minute for fouling Osasuna's Ruben Garcia, who had only the goalkeeper to beat.
Osasuna have failed to score in four straight league games.
They can refocus completely on the Copa del Rey clash at Athletic Bilbao. Osasuna lead 1-0 after the first leg and are trying to reach the cup final for the second time after losing to Real Betis in 2005.
"We should have been able to make good on our advantage," Osasuna defender Aridane Hernandez said.
"We wanted to win this game to boost our confidence after some disappointing performances. And now we have a huge battle on Tuesday."
Osasuna coach Jagoba Arrasate rotated his starting line-up against Mallorca. New Spain defender David Garcia did not play while regulars Moi Gomez, Jon Moncayola, Abde, and Kike Garcia came off the bench.
But the undermanned hosts had little trouble in defence, the strong point of coach Javier Aguirre.
When Osasuna finally did threaten in added time, goalkeeper Predrag Rajkovic made back-to-back saves to deny Moncayola and Abde.
Osasuna forward Chimy Avila missed the match while recovering from a left-leg injury that could rule him out of the Copa semi-final.
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