Messi opened the scoring in the 25th minute, although replays showed the five-time Ballon d'Or winner was in an offside position when he received Ivan Rakitic's pass.
There was little else to question in a majestic display from Barca's talisman, who twice made the most of expert service from Jordi Alba to claim the matchball in the 67th minute - goals 17 and 18 against Espanyol in the top flight.
There were some dicey moments for Valverde's men at the back but the Camp Nou faithful were able to lap up Ousmane Dembele's second half debut with the points safe, even if chants calling for the resignation of club president Josep Maria Bartomeu tempered a goal-laden finale.
Club-record signing Dembele set up Luis Suarez to complete the scoring after Gerard Pique headed a fourth from Ivan Rakitic's 87th-minute corner and Real Madrid's 1-1 draw at home to Levante earlier on Saturday means Barca hold a four-point advantage over the champions after three matches.
Barcelona made all the early running but suffered a scare in the 21st minute.
Sergio Busquets was deservedly booked for cynically pulling back Leo Baptistao after his slack pass threatened to give the Espanyol forward a route to goal.
The opener arrived from the expected source but Messi should have been flagged offside before controlling Rakitic's immaculate pass, cleverly turning David Lopez and rifling into the top corner.
A sublime second almost arrived in the 31st minute – Rakitic adding further to an accomplished showing by gliding towards the box and exchanging passes with Messi to draw a superb save from Pau Lopez.
Valverde's men did not have to wait long to double their advantage as Alba drove an attack from his own half, reacted quickly to a ricocheted return pass from Messi and set up the superstar forward to slot home.
Far from fearing an imminent humiliation, Espanyol gamely responded and Barca goalkeeper Marc-Andre ter Stegen was grasping at air when Pablo Piatti's strike cannoned back off the post two minutes before half-time.
Suarez was back in the Barcelona line-up despite an injury scare while on international duty but was not enjoying himself in front of goal as much as Messi.
The Uruguay star fluffed a shot from Gerard Deulofeu's cross and was denied by Pau at close quarters early in the second period.
A mix-up between Ter Stegen and Alba almost gave Espanyol a lifeline in the 51st minute but Piatti's lofted shot bounced just wide.
Suarez's trials continued as he looped an attempt on to the roof of the net having been set up by Messi – both forwards jogged back into position wearing rueful smiles.
Espanyol were being outplayed but retained a sporadic threat, with a combination of Pique and Samuel Umtiti diverting Baptistao's 61st-minute shot behind.
The points were safe midway through the half when 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.
It was then time for Dembele's triumphant arrival, with fellow new arrival Paulinho on his way shortly afterwards.
Dembele's every touch was cheered and he responded by tearing away from an embattled backline to let Suarez end his personal misery, Pique having revelled in piling further derby misery upon Espanyol shortly beforehand.
The France youngster is at Barcelona to target the summit of the world game and needed to look no further than the match-winner playing inside him to see exactly what that looks like.
