The Brazilian-born striker was not included in Vicente del Bosque's squad on Friday as the paperwork that will make him eligible for the world champions was not completed in time.
However, he again made his case for a future call up with another two strikes to take him top of the La Liga scoring charts with 10 goals, two ahead of Lionel Messi.
It could have been even better for Costa had he not seen a first-half penalty saved by Yoel Rodriguez.
Nolito's cute finish 19 minutes from time made it a nervy finish for Diego Simeone's men, but they held on to move level with Barcelona on 24 points at the top of the table, five points ahead of neighbours Real Madrid.
"The first-half was very complete, but we just needed the goal," said Simeone.
"With complete territorial dominance and when you are playing well offensively the important thing is to finish your chances.
"We didn't do that and therefore we found ourselves in difficulty near the end."
"It wasn't a physical dip, but the fact the opponent grew into the game. It is a normal situation.
"We always had the threat of the counter-attack, but it Celta's good play that forced us back."
Costa had a golden chance to open his account for the day on 25 minutes when Luis was chopped down by David Costas, but Yoel prevailed as he dived low to his left to save the spot-kick.
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