Villarreal, who are seventh, had to come from a goal down to rescue a point at home to regional rivals Elche at the Madrigal.
Fourth-placed Bilbao lost 2-1 to leaders Atletico Madrid at their San Mames stadium on Saturday after Sevilla, in fifth, had their six-match winning streak snapped in a 1-0 reverse at Celta Vigo.
"It's hard to maintain control at this stadium," Sociedad coach Jagoba Arrasate told a news conference at Osasuna's El Sadar arena in Pamplona.
"We had our chances in the second half and they did too," he added. "Looking at it objectively I think a point each was a fair result."
Arrasate's Villarreal counterpart Marcelino Garcia said his players had lacked efficiency in front of goal.
"We went after the win from the first minute, we controlled the majority of the game, showed some good moments and had chances to score," he said.
"We just needed to be a bit more accurate in putting the ball between the posts."
With seven matches left, Bilbao are on course for a place in Champions League qualifying on 56 points, six ahead of Sevilla and Sociedad. Villarreal have 49, nine ahead of eighth-placed Espanyol and Valencia, who are ninth after they lost 3-1 at home to Getafe in Sunday's late kickoff.
Tempers frayed in the final stages of the game at the Mestalla and Valencia captain Jeremy Mathieu was sent off after clashing with Getafe forward Pedro Leon.
In the bottom half of the table, just four points separate Granada on 34 in 12th place from Almeria, Osasuna and Real Valladolid in 17th through 19th.
Real Betis, who host Malaga on Monday, are eight points adrift at the bottom, while Madrid-based Getafe climbed to 16th on 31 points thanks to their first win in 17 matches in all competitions.
- Sports & Recreation
- Gonzalo Castro
- Atletico Madrid