The Brazilian followed up his two goals against Paris St Germain in the Champions League on Tuesday by slotting home after Luis Suarez dummied an Alba cross inside the area to open the scoring after 17 minutes.
With Barca picking holes in the Espanyol defence, Lionel Messi doubled the lead from a tight angle after 25 minutes.
Alba was shown two yellow cards in succession after 53 minutes for a lengthy protest with the referee, but Espanyol failed to apply any concerted pressure on the Barca backline in the remainder of the match.
Xavi came on for the final three minutes for his 500th La Liga appearance for Barca and deep in stoppage time Espanyol’s Hector Moreno was also sent off after being given a second yellow card.
Barca lead La Liga with 81 points, five more than Real Madrid who play Celta Vigo on Sunday.
Later on Saturday, third-placed Atletico Madrid, on 69 points, take on Elche.
“It was a complete game from us and in order to win a derby then you have to play like that,” Barca midfielder Andres Iniesta told reporters.
“The best part of the season is still to come and the hard bit as well. They are all finals from here on and there won’t be much between the teams.”
Espanyol’s defence was cut open from the start with Neymar having a shot from a tight angle saved by keeper Kiko Casilla after just two minutes.
Suarez had a header from close range parried by Casilla and then Neymar flicked a ball by Messi past the keeper but also over the crossbar.It appeared only a matter of time before Barca scored and the goal was expertly executed, demonstrating the superb understanding between their fearsome frontline with Suarez leaving the ball for Neymar to finish.
Rafinha played in midfield with Ivan Rakitic rested and he linked up well as Barca dominated possession.
Suarez was involved in the second goal as he played a ball across the area to Messi who finished clinically past Casilla with little angle to aim at.
Further chances fell to Barca in the second half, notably a shot by Messi that hit a post, and the result never appeared in doubt.
Neymar scored the opener to continue his rich vein of form as Barcelona won a one-sided La Liga derby against Espanyol 2-0 despite the dismissal of Jordi Alba early in the second half on Saturday.
