The home side started off better in the first half and missed their first noteworthy chance 22 minutes into the game when Sergio Canales' effort went just wide.
Betis finally took the lead just after the interval through Bartra who out-jumped the Espanyol defence to head home.
The Catalans pushed for an equaliser but Victor Campuzano was unable to hit the target, while Betis came close twice to scoring a second but neither Canales nor Nabil Fekir could beat Diego Lopez.
Espanyol tried but failed to worry the Andalusians in the remainder of the game and they now sit bottom of the LaLiga Santander table, eight points from safety.
Meanwhile, Betis are in the 13th position with 37 points, 10 points adrift of the European spots.