Espanyol had the better of the few decent chances on offer but Betis survived to open their account for the campaign following 2-1 defeats to Real Madrid and Celta Vigo in their opening two matches.
In contrast to that, Espanyol had enjoyed a good start after taking four points from games against Valencia and Celta, and they will feel they perhaps should have got a maximum points haul from this match as well.
They had a great opportunity to open the scoring in the 16th minute but forward Christian Stuani failed to hit the target with a close-range header following a Simao Sabrosa cross.
That was probably the best chance of the whole game and the only opening of note in the first half, which also saw visiting keeper Guillermo Sara save a Pizzi shot and his Espanyol counterpart Francisco Casilla comfortably deal with a long-range Nosa Igiebor attempt.
It was a similar story in the second half, with Espanyol looking the likelier scorers - although they did survive a scare in the 53rd minute when midfielder Victor Sanchez almost put through his own net.
Stuani again fired over before both Sergio Garcia and Thievy Bifouma were denied by saves from Sara, the second a vital stop when one-on-one with the Espanyol substitute.
Thievy also had a chance to claim the victory for Espanyol in the last minute but was unable to take advantage of the opportunity as Betis held on for a point.