Kevin Gameiro opened the scoring in the early stages of Sunday's encounter, but a spot kick allowed the home side to pick up a point.
The home side had to fight back from behind, with Santi Mina scoring a penalty to cancel out a Kevin Gameiro opener in the first half.
Throughout the 90 minutes, it was Celta which enjoyed the majority of possession against the visiting side, as a slow first half was followed by a a more productive second period.
Despite the home side dictating the game and putting pressure on the deep-lying Sevilla, it was the away team which opened the scoring.
Gameiro broke the deadlock after just eight minutes, taking on a pass from Iago Aspas before the duo played a one-two inside the box which ended with the striker smashing the ball past Sergio Alvarez.
Aspas almost set up another goal for Gameiro on 30 minutes, lashing a deadly cross across the face of goal, only to see the attacker fail to make any contact with it.
Celta looked like carving out a good opportunity shortly afterwards when a good delivery was sent deep into the box, but Diogo Figueiras sent his effort wide.
Center back Alejandro Arribas came close to doubling the guests' lead when he leaped to meet a fantastic diagonal cross from Denis Suarez but the post denied him.
Celta tried to up the pressure in the early stages of the second half. Michael Krohn-Dehli looked like threatening when he cut inside from the left flank but his effort failed to test Sergio Rico.
The home side's breakthrough came moments later, though, when Arribas was judged to halve elbowed Charles in the box. Santi Mina was able to convert the resultant spot kick.
Celta became a much more potent team after the equalizer, attacking with more pace down the flanks than it had previously.
Sevilla threatened in the dying moments, but when its effort was cleared, Celta immediately hit the visiting side with a threatening counter. Fabian Orellana burst into the box but the encroaching Sergio Rico was able to put him off as his shot ended up going over the bar.
The home side had another go at taking the lead deep into injury time, but was forced to settle for a point.