The visitors were in complete control and could have been out of sight shortly afterwards as both Luis Suarez and Messi rattled the woodwork, but the Uruguayan did eventually add his name to the scoresheet on the stroke of the break to all but put the game to bed.
Sevilla had missed the chance to leapfrog Ernesto Valverde's side earlier on Saturday as they were held to a 1-1 draw by Valencia.
It was 2-0 on 26 minutes when Messi picked out Dembele in the Espanyol penalty area and the France global cut back inside to curl the ball past Lopez.More news: France tops OECD list of most taxed countries
Messi was leading Espanyol a merry dance and he set up Barca's second in the 26th minute, twisting and turning defenders on the edge of the box before slicing the back four open with a fine pass for Dembele, who cut inside and fired across Lopez into the top-right corner.
Messi had also set up Dembele's goal in the 26th, sending a well-placed throughball to the French forward.More news: US Attempt to 'Bury' INF Treaty Creates New Risks for Europe - Lavrov
Espanyol went looking for a lifeline at the start of the second half, but Barcelona remained unsafe on the break.
Messi was prevented a hat-trick by a smart Diego Lopez save in the 69th minute, and Espanyol thought that they had registered in the 73rd minute when Duarte converted a Sergio Garcia free kick.
Hernan Perez headed over the crossbar late in the first period as Espanyol searched for a route back into the match, but Barcelona all but secured the points in the final minute of the first period.More news: Trump ghostwriter ridicules belief John Kelly’s replacement will reel president in
However, following a lengthy review from the Video Assistant Referee, the goal was ruled out for a marginal offside.
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