As both Real Madrid and Atletico had dropped points earlier in the day, Barcelona were looking to strike an early blow at the top of the La Liga table.
Messi got the ball rolling with his team's first goal after 26 minutes, although there was a hint of offside when he received a pass from Ivan Rakitic, then sidestepped his marker and fired the ball into the top corner.
The Argentinian star then doubled the lead towards the end of the first half from close range after a ricochet in the penalty area fell to the feet of Jordi Alba, and he completed his hat-trick just after the hour.
A header from Gerard Pique made it 4-0 with just three minutes to go before record-signing Ousmane Dembele, on as a late substitute, put it on a plate for Luis Suarez to get the fifth in stoppage time.
It was Messi's 42nd career hat-trick, 38 of which have come for Barcelona.
"I am happy for Leo who scored three goals and is extraordinary," Valverde said at a post-match press conference.
"We pulled through a complicated game, because these kinds of matches are always tough.
"Despite the result, it wasn't easy. Espanyol fought very well, but we have great players like Messi, who scored three goals, and Suarez, who gave everything like the rest of the team."
This emphatic victory puts Barcelona two points clear at the top of the table, yet to concede a goal in their three La Liga victories, as they prepare to face Juventus in the Champions League on Tuesday night.
Despite Barcelona's positive start, Valverde is still keen to maintain some perspective as they look to maintain their advantage over champions Real Madrid.
"We are at the beginning of the season and the distances are not significant, but it is better to be ahead than behind," Valverde said.
"It does not mean anything, but being ahead is always good."
Valverde decided against throwing Dembele straight into the thick of the action following the 20-year-old's £96.8m move from Borussia Dortmund, but his introduction on 68 minutes was greeted with the loudest cheer of the night from the Nou Camp faithful.
"The idea is to give Dembele minutes, we have a lot of hopes for him and this game was a first step," the Barcelona coach said.
"His team-mates know that he has real quality."