Tomer Hemed netted the game's ony goal after 17 minutes, pouncing on the ball no more than a yard out after Andreu Fontas made a hash of trying to clear an Almeria cross from the right.
Celta dominated large swathes of the game and Fabian Orellana rattled the crossbar with a 20-yard free-kick with visiting goalkeeper Julian well beaten.
The 23-year-old proved the hero in the 72nd-minute, however.
Spain international Nolito had been on the pitch for just five minutes when he had the chance to equalise from 12 yards, but his effort to Julian's left was well-saved by the keeper.
Celta had strong shouts for another spot-kick waved away late on and were ultimately unable to hit back despite raining 19 shots on the Almeria goal.
Victory for the visitors lifts them out of the bottom three to 16th.
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