The winger added to his stunning goal in El Clasico with the winner on Friday night as his rebirth continues under Gerardo Martino
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 pin-point 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.