The lead was doubled on 35 minutes as Messi grabbed his second goal by turning home Gerard Deulofeu's low cross.
Five-time Ballon d'Or victor was in fine form, opening the scoring in the 26th minute, following up again ten minutes later, utilising expert service from Jordi Alba, sealing his hat-trick with more than 20 minutes remaining. But the Argentinean Wizard didn't stop there, he went-on to complete his hat-trick after the break from another Alba cross, putting Barca in a commanding position.
Barca manager Ernesto Vervede introduced new signings Ousmane Dembele and Paulinho for their Barcelona debuts in the second half.
Meanwhile, defending champions Real Madrid were held to a 1-1 draw at home by Levante, meaning Barcelona are top in the La Liga points table.
Espanyol were being outplayed but retained a sporadic threat, with Pique and Samuel Umtiti diverting Leo Batistao's 61st-minute shot behind.
David Ramos GettyImages
However, the hosts were not to be denied in the 26th minute as Messi collected a pass from before firing into the top corner, 1-0.
Suarez was little doubt that Messi was the hero of the hour and handed his team-mate familiar plaudits.
Messi added a second after he burst forward and his pass rebounded to Jordi Alba.
Andre Gomes threaded a delightful ball into Dembele's path who then provided a glorious assist for Suarez.
The victory saw Barca pull further clear of Real Madrid at the top of the early La Liga standings, and after the match Suarez paid tribute to "the best in the world".
Things are looking rosy at the Camp Nou.
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