The Italian outfit came into this game looking to build on their 3-0 victory over Hellas Verona at the weekend, which saw them solidify their position in the Serie A’s top four.
Marco Baroni’s men got off to a flying start too, taking the lead after just five minutes through Mario Gila.
The goal came from a Lazio free-kick in a dangerous position, which Sociedad failed to clear before Gila rifled a first-time strike into the top corner from the edge of the six-yard box.
The visitors went close to finding an equaliser midway through the first half when Luka Sucic expertly controlled the ball just inside the penalty area before bending a left-footed shot towards the far-top corner, but the Croatian’s strike ultimately crashed back of the post.
However, the job got much more difficult for Sociedad with 30 minutes on the clock as Aihen Munoz received a second yellow card for fouling Gustav Isaksen.
Baroni’s side took just two minutes to make their numerical advantage count, doubling their lead through Mattia Zaccagni courtesy of a low, placed effort.
The Biancocelesti scored again shortly after, this time through Valentin Castellanos’ fantastic glancing header from a Nuno Tavares cross.
Imanol Alguacil’s side struggled to gain a foothold in the game after half-time, with Lazio dominating possession, and Baroni’s men seemed more than content with just keeping the ball and seeing out the game.
Still, the hosts still continued to cause problems for Sociedad, going close to a fourth with just under 15 minutes left to play; on this occasion, Pedro Rodriguez, hit the crossbar rather than the back of the net from close range.
However, the away side did manage to pull a goal back in the closing stages of the game through Ander Barrenetxea, heading home inside the six-yard box.
Nevertheless, Lazio managed to see the game out to take their tally to 19 points from a possible 21 and therefore strengthen their grip on first place in the table.
Despite the defeat, Sociedad are all but through to the play-off round, with only a heavy defeat to PAOK and several other results going against them enough to knock them out entirely.