The home side were dominant in the opening stages of the match, with Nolito's strike being blocked inside the first two minutes.
Kevin Gameiro eventually had an effort for the visitors, but his strike failed to hit the target.
The game went through the motions midway through the first half, with Sevilla in the ascendancy towards the final stages thanks to efforts from Gameiro and Carlos Bacca.
The second half saw more of the same, as both sides drove forward in a bid to draw first blood but failing in the final third.
Just as it seemed that the game was going to finish goalless, the home side were awarded a penalty for a foul in the box, which was duly converted by Nolito to break Sevilla hearts and claim the victory for Celta Vigo.