The perfectly struck set-piece goals capped another brilliant performance by Messi, who got past defenders easily and effortlessly put his teammates in a position to score.
Barca led in the 17th minute thanks to the first moment of Messi magic in an astounding display.
Dembele gave the assist for Suarez's goal just before halftime, with the Uruguayan's shot from a tough angle finding the net after going through the legs of Lopez. We deserve a lot of credit for ensuring Espanyol weren't the Espanyol they've been this season.
Espanyol improved after the interval and had a goal disallowed for offside when Oscar Duarte stabbed home Sergio Garcia's cross from close range, but a comeback was never a serious possibility for the hosts.
What does it mean? Yet Barca's efforts to defend the title will take some stopping if they maintain this level of performance, having moved three points clear of the chasing pack.
An overlapping cross from Jordi Alba found its way into the box to the head of Messi at the far post but he was prevented a second by the left post.
Messi has won the award five times in a glittering career but was overlooked at Monday's ceremony with Kylian Mbappe, Antoine Griezmann, Cristiano Ronaldo and victor Luka Modric all receiving more votes.
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"To beat Barca you have to play a flawless match and that has not happened".
Messi was in fine form against derby rivals Espanyol.
As is predominantly the case, Lionel Messi was the star of the show for Barcelona as the Spanish side swatted away the challenge of Espanyol in a 4-0 La Liga thrashing at the RCDE Stadium on Saturday night.
Messi's free-kick was also the eighth set-piece he has scored this year in LaLiga, three more than any team in Europe's top-five leagues have collectively managed in 2018.
Espanyol have now lost four league games in a row, their strong start to the season fading badly.