The hosts, who spent the 2016-2017 season in the second division, have posted two wins and three draws for 9 points, an identical record to neighbors Valencia on Thursday, reports Efe news agency.
Levante started strong before gradually yielding possession to Sociedad while remaining alert for openings on the counter.
Just as the squads looked set to end the first half scoreless, Levante's Chema connected with a cross from Jose Luis Morales to put the home side ahead 1-0.
Juanmi had an opportunity to equalize for Sociedad in the opening minutes of the second half, but his shot sailed over the crossbar.
Sociedad kept Levante pinned in their own end, yet their dominance did not translate into goals and the passing of the minutes led the visitors to take more chances, which in turn made them more vulnerable to counterattack.
With 15 minutes left in regulation, the referee awarded Levante a penalty after Alvaro Odriozola was brought down in the area and Morales converted from the spot to make it 2-0.
The final goal came in the 88th minute, when Enis Bardhi connected on a direct free kick after Sociedad's Diego Llorente was sent off for a second yellow card.
Sociedad, with three wins and two defeats, have 9 points, but trail fourth-place Valencia and fifth-place Levante on goal difference.
In Thursday's other matches, Celta and Getafe drew 1-0 and Villarreal and Espanyol deadlocked 0-0.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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