The victory by last season's UEFA Cup winners keeps Barcelona's lead at the top of the table down to one point after the reigning Spanish champions thrashed Recreativo Huelva 3-0 on Saturday.
Brazilian striker Nene put Celta ahead after just seven minutes, after the hosts had done all the defending early.
However, Sevilla’s Danish midfielder Christian Poulsen equalised after the 30 minute mark with a stunning long range effort.
Some slack defending then put Sevilla in the lead after Adriano was allowed the space to score.
It was then Sevilla’s goalkeeper Andres Palop who played the role of hero after he ensured his side would leave with all three points after he saved a penalty in the dying minutes.
“With only a one goal advantage, these sort of things can happen but I think we were superior and we deserved to win," reflected Sevilla coach Juande Ramos.
"When the referee blew his whistle for the penalty, I was reminded of all the occasions when Sevilla have had these sort of opportunities and we've thrown them away. This time it was the opposite situation."
At the other end of the table, the fortunes of Real Sociedad are yet to change as the remain winless and on the bottom of the table.
Villarreal's Rodolfo Arruabarrena did the damage this week as he got the only goal of the game to snatch an important victory for his side.
Miguel Angel Lotina took over at the helm at the San Sebastian on Friday but the new coach was unable to produce the desired result.
"At least the fans were supporting the players. We know we are in a difficult situation and that we have to improve but I saw some encouraging signs in this game," said Lotina.
Real Betis' president Jose Leon Gomez is also feeling the heat after his side lost to Real Mallorca 1-0 to also remain in relegation trouble.
"I know my job is in jeopardy but that's football and I'm a footballing man," admitted Betis coach Javier Irureta.
Getafe notched up their third successive victory with an impressive 2-0 win over Deportivo La Coruna, their goals coming in either half from Manu Del Moral and Nacho Perez.
Getafe, deal with Depor's new kit,
and then record a win
Ronaldinho scored twice to help Barcelona extend their lead at the top with a 3-0 win over Recreativo Huelva on Saturday.
Real Madrid were stunned at Gimnastic Tarragona when the newly-promoted side went ahead with a 29th-minute penalty from Abel Buades but fought back to win 3-1 win and move up to third.
While Valencia slipped up ahead of Tuesday's visit in the Champions League to Shakhtar Donetsk and went down 1-0 at Racing Santander on Saturday through a Pedro Munitis header.