Trailing 2-0 to the visitors midway through the second half, Valencia drew on all their reserves of strength to claw their way back into the match and clinch the draw that allowed them to return to the top ahead of Real Madrid.
With five games to go Valencia and Real both have 70 points, but Rafa Benitez's side lead the table by virtue of their better head-to-head record against the reigning champions.
Barcelona stretched their unbeaten run to 15 matches and moved up a place into third on 63 points, two ahead of Deportivo Coruna, after a classy 3-0 win over Malaga at the Nou Camp.
Argentine striker Javier Saviola opened the scoring when he guided in at the near post after a superb pass from Luis Garcia and returned the favour for the winger to notch the second four minutes later.
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The Catalans meet Real Madrid, who edged neighbours Atletico 2-1 on Saturday, at the Bernabeu next weekend, while Valencia face a tricky trip to fifth-placed Athletic Bilbao.
Earlier, basement side Murcia returned to the second division after just a season in the top flight when they slumped to a 1-0 defeat at home to Real Betis.
John Toshack's side are now 16 points behind Real Mallorca, who sit just above the relegation zone after their 2-1 defeat at home to UEFA Cup semi-finalists Villarreal.
Fellow strugglers Espanyol and Celta Vigo both kept alive their hopes of survival with away wins over Osasuna and Albacete respectively.
The performance of the day came from Sevilla forward Julio Baptista who grabbed four goals in his side's 5-2 win at home to Racing Santander, a victory that put them back in the hunt for a UEFA Cup place.
DOMINATED POSSESSION
Valencia, anxious not to allow Real Madrid to displace them at the top, took the initiative from the off and pinned Sociedad back in their own area for most of the first half.
But although they won a string of corners and dominated the possession, the home side found it difficult to create any clear scoring chances.
Sociedad, who attacked little in the first half, took the lead out of the blue 20 minutes after the break when midfielder Xabi Alonso intercepted a Valencia throw-in and sent a swirling 20-metre shot over keeper Santiago Canizares and into the net.
Minutes later Valencia were dealt another blow when defender Roberto Ayala was harshly adjudged to have fouled Sociedad forward Oscar de Paula in the area and Valery Karpin cracked in the resulting spot kick.
But Valencia hit back four minutes later when winger Vicente controlled a long cross from Angulo and drilled in low past Alberto to make it 2-1.
Benitez's men poured forward for the remainder of the match as they desperately searched for the equaliser and they finally got their reward a minute into injury time.
Mista snapped up a loose ball on the edge of the area and crashed an unstoppable drive in off the underside of the bar and across the line to score his 19th goal of the season and claim the all-important point.
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