The draw leaves Barca still leading with 35 points from 16 games but Real Madrid, on 34, can take their place at the top if they win at Valencia on Sunday, perfectly setting up a mouth-watering midweek clash between the two giants at the Camp Nou.
Antoine Griezmann levelled for Barca in the 38th minute, scoring against the club where he began his career by nonchalantly scooping the ball over Alex Remiro after being played in by Luis Suarez in a sweeping counter-attack.
Suarez put the Catalans ahead in the 49th minute, passing a lay-off from Lionel Messi into an empty net.
Sociedad levelled shortly after the hour mark, as Barca goalkeeper Marc-Andre ter Stegen failed to properly punch away a cross from Nacho Monreal and Swedish youngster Alexander Isak pounced on the loose ball to smash it home from close range.
"Both teams had our moments and our chances and either side could have scored a third goal," said Griezmann.
"It's a shame we could only draw. We gave everything but now we have to learn, improve and focus on the Clasico. They made a very good start and we got our tactics wrong but in the end we fixed it and we created chances to win the game."
Real Sociedad are fourth in the table on 28 points, three points behind third-placed Sevilla.