Messi added a second after he burst forward and his pass rebounded to Jordi Alba.
Real Madrid fell four points adrift and sits in sixth place after a second consecutive draw at Santiago Bernabeu Stadium, 1-1 with newly promoted Levante. At just 20 years of age, Espanyol left back Aarón Caricol will be tasked with keeping the world's best player quiet.
The same two players combined again nearly immediately as Rakitic slalomed through the defence and played a sharp one-two with Messi before forcing a good low save from Lopez.
Espanyol almost pulled a goal back just before the break when Pablo Piatti rattled the upright from the edge of the box.
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.More news: Brussels to leave Britain full responsibility for sorting Irish border after Brexit
Valverde did not disclose whether Dembele would be handed a debut and was similarly non-committal over the potential inclusion of Luis Suarez, who is yet to play in LaLiga this season but turned out twice for Uruguay during the worldwide break following a knee injury. That could have been a lifeline for Espanyol. Set up Messi's first goal (and Pique's), nearly scored a brilliant goal of his own and drove forward from midfield time and again.
Espanyol was being outplayed but retained a sporadic threat, with a combination of Pique and Samuel Umtiti diverting Baptistao's 61st-minute shot behind. A ricochet falls nicely for Alba inside the box, who crosses into the path of Messi, who finishes underneath the keeper on the slide. While the club have maintained a winning momentum so far, it remains to be seen how the worldwide break has its effect.
Valverde has enjoyed a strong start to life at Barcelona, with the Catalans winning all three of their opening leagues games, scoring eight goals and keeping three straight clean sheets. Andres Iniesta will be rested having played two games for Spain and a big clash against Juventus in the Champions League fast approaching.
66' GOAL! Barcelona 3-0 Espanyol: It's all about Messi this evening!
Barcelona won 34 of the last 36 possible points against Espanyol in La Liga. Lionel Messi was the difference in Barcelona's last La Liga game, netting a brace against Deportivo Alaves.