De Jong struck after only eight minutes to get Sevilla off to a flying start but his effort was cancelled out by Coutinho just two minutes later.
The result maintained both sides' unbeaten starts to the season.
Sevilla, with coach Julen Lopetegui in the stands due to a touchline ban, made the early running and had already gone close through Ivan Rakitic when De Jong smashed home the opener following a corner.
Yet it was a lead they could not maintain as Barca equalised almost immediately through Coutinho.
It was the Brazilian's first goal since returning to the club following last season's loan at Bayern Munich.
Sevilla threatened again when veteran Jesus Navas got forward, but Fernando was unable to get a touch to his ball across goal.
Lionel Messi cut in from the right and fired a shot just wide for Barca on the stroke of half-time.
Sevilla almost reclaimed the lead just after the hour when a Youssef En-Nesyri effort was deflected onto a post. Former Barca star Rakitic also missed the target before En-Nesyri headed another good chance over.
Frenkie De Jong had a late chance for Barca but Sevilla held on for a deserved point.