Sevilla initially looked the more determined side, and Vicente Guaita had two quickfire moments of alarm, firstly blocking a near-post effort from Adria Pedrosa, before grasping a powerful Ramon Martinez header from a corner.
Celta then kicked on, and barely a minute after forcing a reflex save from Orjan Nyland, Ilaix Moriba finally netted his first Celta goal when he turned and fired into the bottom-left corner, after being fed by Williot Swedberg.
Celta were expected to press on and take the initiative. However, Sevilla found reserves of energy and were the more menacing side from there, particularly when Dodi Lukebakio drew an impressive save from Guaita with a header on goal. And there was an unwelcome twist for the visitors when Loic Bade was withdrawn through injury.
But fortune proved kinder to Sevilla in first-half stoppage time, when Marcos Alonso was penalised and sent off for a goal-denying handball on Peque’s touch inside the area.
Nemanja Gudelj stepped up and fired powerfully home from 12 yards, but was forced to retake due to striking before the whistle. On the second attempt, the Serbian rocketed his penalty - and his first goal of the season - into the top-left corner to ensure parity at the break.
The second half didn’t initially live up to the same dramatic qualities as the first. Passages of Celta play continually broke down, while Sevilla seemed content to bide their time in the hopes of wearing down their numerically disadvantaged hosts.
Celta didn’t oblige, though, and in the 65th minute, they went back in front against the odds. A well-worked Fran Beltran cross from the right proved too high for Pablo Duran, but it was met by Oscar Mingueza, who hit the ball home at the far post to send Balaídos into raptures.
The dying minutes were packed with tension, but moments after Guaita produced a stunning save from Kike Salas’ effort, a botched Gudelj interception from Iker Losada’s ball forward allowed Borja Iglesias to sneak in and loft in his 10th goal of the campaign.
That put the proverbial top hat on a vital win for Celta in the race for European football - and not even a last-second consolation from Salas via a Guaita spill could soothe Sevilla’s pain. Their wait to secure a top-flight place continues, though a win over Las Palmas on Tuesday should complete the job.
Flashscore Man of the Match: Oscar Mingueza (Celta Vigo)