Hopes of progressing to the Europa League quarter-finals this season could have been sunk following Thursday's 2-0 home defeat to Betis, but Sevilla's Primera Division form could yet see them playing Champions League football next season.
A brace from Kevin Gameiro, one a penalty, plus further goals from Ivan Rakitic - also from the spot - and Diogo Figueiras earned them victory over Real Valladolid and improved their winning streak in La Liga to four matches.
It also lifted them to within seven points of fourth-placed Athletic Bilbao, who face a tough trip to fifth-placed Villarreal on Monday night.
Valladolid netted a consolation through Javi Guerra but it did little to affect the outcome as his side remained stuck in the bottom three.
The visitors created a huge upset with last week's win over Barcelona and, with Sevilla wounded from their first-leg loss to Betis, they will have been quietly optimistic heading to the Ramon Sanchez Pizjuan.
They also created the first openings of the match with Marc Valiente and Stefan Mitrovic going close early on, but after that it was pretty much all Sevilla.
Unai Emery's in-form side were unlucky to have lost to Betis after dominating that match, but they ensured it was a different story on Sunday.
Diogo had already brought a flying save out of Diego Marino when the hosts took a 22nd-minute lead from the spot.
Lluis Sastre clumsily sent Marko Marin crashing just inside the box and Rakitic sent Marino the wrong way from 12 yards.
Sevilla continued to push and doubled their lead in the 41st minute when Marin threaded a pass into Gameiro and he lashed a rising shot into the near top corner.
Sevilla keeper Antonio Beto then ensured his side would go into the break with that two-goal lead intact as he turned Valdet Rama's 25-yard free-kick onto the post with a brilliant one-handed save.
It was Marino's turn to produce an impressive stop at the start of the second half to deny Gameiro following a well-worked free-kick routine, but the Valladolid keeper was then at fault as Sevilla made it 3-0 in the 66th minute.
Matino's attempted to pass a goal-kick to one of his defenders but the ball was intercepted by Jose Antonio Reyes, whose subsequent cross hit the arm of Mitrovic and led to the second penalty of the match.
This time Gameiro took it and, like Rakitic before him, comfortably beat Matino.
Reyes was also heavily involved in the next two goals - one for Sevilla and one for Valladolid.
The former Real Madrid winger picked out Diogo to side-foot home Sevilla's fourth in the 74th minute, but then 60 seconds later he was robbed on the edge of his own area by Guerra, who then lashed his shot past Beto.
It was a goal that should have been avoided but, fortunately for Reyes, it was not costly.