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.
Victory in the Catalan derby, the 21st consecutive league triumph for the champions at the Nou Camp going back to last season, put Barca four points clear of second-placed Atletico Madrid with 34 out of a possible 36 after 12 matches.
The only game they failed to win was a 0-0 draw at Osasuna on October 19.
Atletico host Athletic Bilbao on Sunday after Real Madrid, five points behind in third place, visit Rayo Vallecano on Saturday.
In-form forward Alexis, who scored brilliantly in last week's 2-1 'Clasico' win at home to Real, grabbed his seventh league goal of the season in a match against eighth-placed Espanyol that Barca dominated without creating many chances.
Brazil forward Neymar somehow managed to thread a cross from the left through the legs of two defenders after 68 minutes and Alexis pounced to earn his side victory.
"It was a very tough, physical match for us," Alexis told Canal Plus television. "We are going home satisfied because they were three very important points.
CLOSED RANKS
"They closed ranks at the back but I am pleased with the goal. I was in the right place."
Neymar's Brazil team mate Dani Alves volleyed against a post before halftime but the home side's lack of penetration against a stubborn Espanyol defence will be a matter of concern for coach Gerardo Martino ahead of Wednesday's Champions League tie with AC Milan.
"Their game plan to deny us space made things difficult, it's something we always say but that's the way it is," said Barca and Spain playmaker Andres Iniesta.
"We tried to inject as much pace as possible to create chances quickly."
On Messi's barren run, Iniesta said: "I don't think the problem has anything to do with any individual player.
"The team works when everyone does their job and doesn't work when we don't all show up. We just have to keep improving."
Barca lead Champions League Group H with seven points from three games. Milan, who held the Catalan side to a 1-1 draw at the San Siro last month, are second on five points.
Celtic have three points and Ajax one ahead of their clash in Amsterdam on Wednesday.
(Reporting by Iain Rogers; editing by Tony Jimenez)
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