Xavi, also back from injury, wasted a penalty three minutes after halftime when he sent his spot-kick wide after Fabregas had been fouled in the area by Elche’s Ionut Sapunaru.
However, Pedro took Andres Iniesta’s through ball and squared for Alexis to fire into an open net in the 63rd minute.
Moments later, Alexis earned his free-kick from a foul outside the penalty area that the Chile forward promptly curved over the defensive wall with a right-footed strike.
The game’s only negative for Barcelona was defender Marc Bartra apparently hurting his leg late on.
Sociedad took control of the back-and-forth match at the Estadio Anoeta when Antoine Griezmann followed up his own rebound from long range for this 12th league goal of the season two minutes before halftime.
Bilbao sought an equalizer, but it was Sociedad’s Ruben Pardo who capped the victory in stoppage-time.