A poor run of form had threatened to kill Sevilla's chances of securing a place in Europe's premier tournament but they dismantled usually solid Getafe with goals from Lucas Ocampos, Fernando Reges and Jules Kounde.
Victory means Sevilla move up to third in La Liga, one point above Getafe and three ahead of Real Sociedad in fifth, although la Real have a game in hand.
Getafe might still have been feeling the effects of their superb 2-0 win over Ajax on Thursday in the Europa League as Jose Bordalas' side lacked the defensive discipline that has thrust them into the mix again for a Champions League spot.
Sevilla, meanwhile, were arguably the favourites to finish fourth at the start of the season and former Spain coach Julen Lopetegui will have been relieved to return to winning ways, just as the pressure on him was beginning to mount.
This was only their second victory in La Liga since the start of the year.
Ocampos scored Sevilla's opener two minutes before half-time, teed up by Sergio Reguilon after Getafe's Djene Dakonam slipped.
Getafe pushed for an equaliser but were undone by two goals in eight minutes shortly after the hour as Fernando Reges bundled in Luuk de Jong's smart header to the back post before David Soria failed to prevent Jules Kounde's shot creeping inside the far post.