Just two minutes later, Sevilla doubled their lead when Varas palmed the ball straight back into the penalty area, when Negredo was once again waiting to fire home.
Celta pulled one back five minutes before the break when Aspas darted into the box before finding Augusto Fernandez, who made no mistake with his finish.
They almost made it 2-2 three minutes later when Fabian Orellana picked the ball up inside the box, but his eventual effort thumped back off the Sevilla crossbar.
It was the hosts who got the game's crucial fourth goal, and it came from another Varas mistake. Gary Medel's shot should have been easy for the keeper to collect, but he let it slip through his hands and into the net.
Negredo completed his hat-trick two minutes later, picking up a loose ball in the area before thumping a shot past Varas to complete the scoring.