Despite dominating possession for large spells of the match, the leaders were frustrated by a well-organised visiting defence.
Alexis eventually broke the deadlock in the 69th minute when he tapped home from a pinpoint Neymar pass.
Barcelona have now won 21 league matches in a row on home soil and boast a four-point advantage over nearest rivals Atletico Madrid, who play on Sunday.
Gerard Pique returned from a hamstring injury but there was no place for Carles Puyol as Gerardo Martino made six changes from Tuesday’s 3-0 victory at Celta Vigo.
Espanyol made four alterations of their own, with Gabriel Torje among the players to come in.
After withstanding some early pressure from the hosts, Espanyol got a sight of goal in the sixth minute but Torje sent his eventual effort wide.
Alexis had an 18-yard strike punched away by Kiko Casilla at the other end as Barca went in search of a breakthrough.
With Martino’s men dominating possession, Dani Alves nodded the ball back for an advancing Alexis in the 28th minute, but the Chilean failed to get any purchase on a strike that was charged down in the penalty area.
The visitors could – and possibly should – have broken the deadlock against the run of play 10 minutes prior to the break. David Lopez was sent through one-on-one with Victor Valdes, only to be denied by the goalkeeper’s outstretched boot.
On the stroke of half-time, Alves exchanged passes brilliantly with Sergio Busquets just outside the penalty area before fizzing an 18-yard effort against the left-hand upright.
Barcelona continued to enjoy the lion’s share of the ball after the break, and Lionel Messi drew a superb diving save from Casilla in the 54th minute as he got his head to a looping Alves cross from the right.
With the hosts finding it difficult to break down a resolute Espanyol backline, Neymar created an angle for himself on the edge of the 18-yard box and curled a shot inches wide.
Barca finally broke the deadlock in the 68th minute as Neymar threaded a pass through the legs of two defenders to find a grateful Alexis, who was left with a simple tap-in at the far post.
Sergio Garcia forced Valdes into a save from close range with 10 minutes left as Espanyol chased an equaliser, before Messi curled a free-kick narrowly wide late on.
