Barca conceded for the first time this season in the eighth minute. Sevilla went with the same corner routine they used earlier in the match and Suso beat Ansu Fati before crossing towards Jules Kounde. The defender got up and challenged for the ball, which dropped for Luuk de Jong to slam high past Neto.
The Blaugrana equalised just two minutes later. Coutinho picked out the top-right corner after Jordi Alba squared to the Brazilian from Lionel Messi's beautiful lofted pass.
In the 21st minute, Barca won the ball back high up the pitch and Sergio Busquets played a first-time pass to Fati, who followed suit to play in Griezmann. Diego Carlos was recovering in defence, but the forward got his shot off, prodding narrowly wide.
Messi came close just before the interval. The Barca number 10 picked up the ball on the right flank and cut inside, looking to curl a shot into the far corner. A team-mate almost got a touch, too, but the ball drifted wide.
A low Youssef En-Nesyri cross from the left clipped Ronald Araujo's unwitting foot and bounced onto the frame of the goal and away.
Sevilla were pushing hard and Kounde headed wide twice in quick succession before Jesus Navas whipped in the cross for En-Nesyri, who headed over the top.
In the 81st minute, Messi took aim from 20 yards. It was a low strike that was close to Bounou, but the goalkeeper could only parry clear.
Shortly afterwards, a ball into the box was met by Frenkie de Jong first time, his prod deflecting agonisingly wide with Bounou wrongfooted.
New signing Trincao had a chance to win it for Barca in the closing stages. Barca had exploited the space behind Marcos Acuna on a couple of occasions and Trincao had a clear run from the wing through on goal. Bounou was out, though, and got down to make a low stop as the points were shared.