Messi scored two stunning free kicks to make it 23 derby goals, while fellow forwards Dembele and Luis Suarez also registered at the RCDE Stadium. A goal in each half with an assist in between saw the 5th best player in the world, according to France Football, break another La Liga record.
The win sees Barcelona go three points clear at the top of the LaLiga table, whilst Espanyoldrop to ninth.
The Barcelona captain, who finished only fifth in this year's Ballon d'Or vote, curled in another superb dead-ball strike on 65 minutes to cap a fine individual and team performance.
Substitute Philippe Coutinho was denied the icing on top of the cake by Lopez's strong left hand shortly after coming on, before one incident pretty much summed up Espanyol's night.
Barcelona were caught out at the back in the 74th minute when Duarte stabbed the ball in at close range from a free-kick.
Dembele turned provider this time, slipping his fellow forward in in the left-hand channel, with Suarez doing brilliantly to hold off the challenge of a defender and somehow squeeze a finish through the legs of Lopez and into the far corner from the narrowest of angles.
Espanyol went looking for a lifeline at the start of the second half, but Barcelona remained unsafe on the break.
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Espanyol looked for a way back in to the match as Duarte's downward header at the far post was blocked by Marc-Andre ter Stegen.
Victor Sanchez headed over the Barcelona crossbar 10 minutes from time as Espanyol continued to search for a goal, and it nearly arrived when Baptistao struck towards the far corner, but the ball just deflected wide.
Barca's front three were all in fine form but Messi was the conductor at the heart of all their play.
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