The game was all but over after just 25 minutes as the hosts raced into a three goal lead which was never seriously threatened.
Former Arsenal defender Silvinho put through his own net after 12 minutes to start Celta's decline, and two goals in two minutes from Walter Pandiani (pictured) and Pedro Munitis put Depor out of sight.
Celta's miserable night was compounded by Eduardo Berizzo's dismissal minutes from time.
Real Valladolid also suffered a potentially fatal blow in their bid to escape the drop after slipping to a 1-0 defeat at Real Betis.
Brazilian midfielder Marcus Assuncao settled the game with a strike fifteen minutes from time.
The result means that Valladolid will be relegated if Espanyol win at Mallorca on Sunday, while Celta will be relegated if Racing Santander also avoid defeat at Barcelona.
Atletico Madrid's game with Zaragoza was postponed following the death of owner Jesus Gil.
Match summaries:
Atletico Madrid P-P Zaragoza
Deportivo La Coruna 3-0 Celta Vigo
Real Betis 1-0 Valladolid
