After continuing to press Barca high up the pitch during the early exchanges, Sevilla capitalised on a mistake from Sergi Roberto and Vitolo slid his close-range effort under the onrushing Ter Stegen, to the delight of a raucous home support.
Vietto turned provider on the half-hour mark as he crossed for Pablo Sarabia, who found himself unmarked with only the German keeper to beat, but the midfielder produced a bizarre flick backward as the hosts squandered the opportunity.
Despite Sevilla dominating much of the first period, Barcelona were able to draw level after Neymar cut inside from the left flank and teed up Messi, whose low curled finish beat Sergio Rico at full stretch.
After the interval, Luis Enrique's side started to get more of a foothold in the game as Rico denied bothLuis Suarez and Messi with two saves in as many minutes.
Just after the hour mark, Barca's pressure finally told as Messi drew in defender before finding Suarez on the right of the box and the former Liverpool star slotted his effort through the legs of the Sevilla keeper.
On 72 minutes, Suarez almost netted his second of the evening after latching onto Neymar's through ball before rounding Rico and placing his strike just wide of the left post.
Despite a near miss in the latter stages from Steven N'Zonzi after Ter Stegen flapped at a cross and a penalty appeal for a supposed handball by Samuel Umtiti, Sevilla were unable to produce a late equaliser and slumped to only their second defeat of this campaign under new coach Jorge Sampaoli.
