It was a bittersweet game for the champions who looked far more like their old selves ahead of a tough run of fixtures, but lost Lionel Messi to injury in the first half.
Barcelona got off to the perfect start at the Camp Nou, as Coutinho opened the scoring with just two minutes on the clock. Messi played in the Brazilian inside the box, and he curled home a brilliant finish into the top corner.
Sevilla almost hit back within minutes of going behind. Guilherme Arana beat Marc-Andre ter Stegen with a shot, but the ball crashed against the woodwork and Barca were saved.
Messi added a second after just 12 minutes. Luis Suarez picked out Messi on the right, and he cut inside and curled the ball low past goalkeeper Tomáš Vaclík.
Barcelona were looking in great shape but suffered a massive blow when Messi fell awkwardly and injured his arm. The captain was clearly in pain and couldn’t continue, with Ousmane Dembele replacing him.
The second half saw plenty of chances in an open game. Luis Suarez saw a strike from range just flick off the outside of the post, Jordi Alba then survived a penalty appeal after Jesus Navas’ cross hit his outstretched arm.
Ter Stegen then came to the rescue with a brilliant double save. The German first tipped away Andre Silva’s header and then smothered Franco Vazquez’s follow-up.
Minutes later and Suarez secured the three points. The striker was sent clean through only to be pulled down by Vaclík. Up stepped the Uruguayan to send the goalkeeper the wrong way and seal the win.
Sevilla did manage to pull one back through Sarabia’s strike. His shot took a big deflection off Clement Lenglet and beat Ter Stegen.
The visitors kept going and Ter Stegen made another wonderful double save from Sarabia and Ben Yedder late on, before Rakitic hit Barca’s fourth with a sweetly-struck volley. Luis Muriel had the final say with another goal for Sevilla, but it was to prove only a consolation.
Barcelona: Ter Stegen; Semedo, Piqué, Lenglet, Alba; Rakitic, Busquets, Arthur (Sergi Roberto); Messi (Dembele), Suárez (Munir), Coutinho
Goals: Coutinho (3’), Messi (12’), Suarez (63’), Rakitic (89’)
Valencia: Vaclik; Carriço, Kjaer, Gómez; Navas, Sarabia, Banega, Vázquez (Roque Mesa), Arana; André Silva (Muriel), Ben Yedder
Goal: Sarabia (78), Muriel (91’)