In a season which has seen several sides go top, including Granada, Real Sociedad have 23 points from 13 games with Barcelona and Real Madrid just a point behind with two games in hand and both playing on Saturday.
Leganes striker Mikel Merino got the away side off the mark in the 63rd minute before before Moroccan Youssef En-Nesyri equalised with a header on 78.
"I see long faces both inside the dressing room and out of it, but we have to be happy," said Real Sociedad coach Imanol Alguacil.
His opposite number Javier Aguirre overseeing his first point in his first match in charge was also positive.
"We're still bottom and that's how it goes sometimes but we have got a point at a difficult ground against a strong side who are top of the league and I'm really happy for the boys," said Aguirre.
Leganes have just six points and will be locked in a long struggle to climb out of the relegation zone.