The three points, which were gained courtesy of a hat-trick from Lionel Messi and late goals from Gerard Pique and Luis Suarez, have seen Barcelona move to the top of the table, four points clear of the reigning champions Real Madrid.
Ivan Rakitic recovered from a muscular problem to start for the hosts, while Luis Suarez returned from a knee injury to take his place in the final third of the field.
As for Espanyol, Victor Sanchez overcame an injury to captain the visitors, but Diego Lopez, Oscar Duarte and Javi Lopez all missed out. Further forward, Leo Baptistao was joined by Gerard Moreno and Pablo Piatti in a 4-3-3 formation, while summer signing from Real Madrid Mario Hermoso made his debut at centre-back.
As expected, it was Barcelona that took control of the early possession, but aside from a Messi effort, which flew harmlessly over the crossbar, Espanyol restricted the hosts to very little inside the opening 15 minutes.
Luis Suarez attempted to find the top corner with a long-range free kick in the 19th minute, but Espanyol goalkeeper Pau Lopez was on hand to make a smart save as the score remained goalless at Camp Nou.
Barcelona's possession statistics reached 80% at the midpoint of the first period, and that translated into a goal in the 26th minute when Messi collected a super pass from Rakitic inside the Espanyol box before finishing into the top corner. Replays, however, showed that the Argentine was in an offside position.
Rakitic should have doubled Barcelona's lead less than five minutes later after driving into the Espanyol box, but the Croatian, who overcame a muscular problem to start, could not find a route past Pau Lopez.
Barcelona did have their second in the 36th minute, however, when Jordi Alba squeezed a low cross into Messi, who simply could not pass up the opportunity to find the back of the net.
Espanyol came close to registering late in the first period when Piatti worked a yard of space inside the Barcelona box before attempting to find the corner of the net, but the ball smashed off the post as the two-goal separation remained entering the half-time break.
Luis Suarez almost made it 3-0 early in the second period after meeting a low cross from Rakitic, but Pau Lopez was on hand to keep out the Uruguay international's inventive flick.
Espanyol then had a wonderful opportunity in the 51st minute when a mistake from Alba presented Piatti with the ball inside the Barcelona box, but the Argentine just looped the ball wide of the far post.
Luis Suarez passed up another chance in the 55th minute after Messi had found his fellow South American, before Baptistao had one deflected wide of the post down the other end as the score stayed at 2-0 entering the final 30 minutes.
Barcelona scored their third in the 67th minute, however, when a clever pass from Alba found Messi unmarked inside the Espanyol box, and the 30-year-old completed his hat-trick with a brilliant finish into the far corner.
Dembele was finally given the nod in the 68th minute as the France international entered the field for his Barcelona debut, with Deulofeu leaving to a standing ovation following another impressive performance.
Paulinho almost scored a fourth for Barcelona 10 minutes from time after meeting a super ball from Luis Suarez, but the Brazilian could only turn wide of the post, before Marc-Andre ter Stegen made a flying save to deny Didac Vila down the other end of the field.
Barcelona scored their fourth in the 87th minute when Pique headed home from close range, before Luis Suarez made it 5-0 in the 90th minute with a well-placed finish after Dembele had delivered a brilliant cross into the Espanyol box.
Next up for Barcelona is their Champions League group opener against Italian champions Juventus on Tuesday night, while Espanyol will continue their La Liga campaign at home to Celta Vigo on September 18.