Deportivo La Coruna return to La Liga
Substitute Xisco bundled in the winning goal in the 70th minute and Deportivo withstood a late surge from the visitors at the Riazor to move on to 88 points from 41 matches with one game left to play.
The Galicians were four points ahead of regional rivals Celta Vigo and six above third-placed Valladolid.
The top two in the second division secure automatic promotion, while third through to sixth go into a play-off for the last promotion spot.
Depor were relegated in 2011 after a 20-year spell in the top flight, when they won their only La Liga title in 2000 and the King's Cup in 2002, and regularly competed in European competition.