Five-time Ballon d'Or winner 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.
Club-record signing Ousmane Dembele made his debut, setting up Luis Suarez to score Barcelona's fifth in the 90th, coming just moments after Gerard Pique headed a fourth in the 87th-minute.
Barcelona made all the early running but suffered a scare in the 21st minute when Sergio Busquets booked for cynically pulling back Leo Baptistao after his misplaced pass threatened to give the Espanyol forward a route to goal.
From there the floodgates opened, and although Messi should have been flagged offside, no call came as he controlled Ivan Rakitic's pass before cleverly turning David Lopez and rifling into the top corner.
Valverde's men did not have to wait long to double their advantage as Alba drove forward, setting up the superstar forward to slot home his second.
Suarez was back in the Barcelona line-up after an injury scare while on international duty with Uruguay, but was not enjoying himself in front of goal as much as Messi, fluffing shot from a Gerard Deulofeu's cross before being denied by Pau early in the second period.
A mix-up between Barca keeper Marc-Andre ter Stegen and Alba almost gave Espanyol a lifeline in the 51st minute, but Piatti's shot bounced wide, with Gerard Pique and Samuel Umtiti called into action to divert
Espanyol were being outplayed but retained a sporadic threat, with Pique and Samuel Umtiti diverting Leo Batistao's 61st-minute shot behind.
Messi and Suarez played one-twos into the box and the ball broke to Alba, with the mercurial Argentinian on hand to convert the cutback once more to take the lead for three, with Dembele introduced shortly afterwards, followed by fellow new signing Paulinho shortly afterwards.
Pique piled further misery before Dembele's helped Suarez end his misery, sealing the match right on the end of regular time.