The victory in the Catalan derby at the Nou Camp put unbeaten champions Barca four points clear of second-placed Atletico Madrid, with 34 points out of a possible 36 after 12 matches.
Their only dropped points came in a 0-0 draw at Osasuna on Oct. 19.
Atletico host Athletic Bilbao on Sunday after Real Madrid, five points behind in third, visit Rayo Vallecano on Saturday.
Alexis grabbed the only goal of a match that Barca dominated without creating many chances.
Neymar somehow managed to thread a cross from the left through the legs of two Espanyol defenders and the Chilean was well positioned at the far post to tap the ball into the net after 68 minutes.
The biggest surprise of the night was that Barca's World Player of the Year Lionel Messi failed to score for a fourth straight league match in which he played the full 90 minutes, the Argentina forward's worst run in almost six years.