Striker Aspas struck in the 83rd minute with a left-foot finish into the bottom right following Roberto Lago’s pass.
With Edu Oriol particularly profligate, Zaragoza were wasteful in front of goal, failing to find the net with 14 efforts, although only three were on target.
The visitors, meanwhile, managed to get four on target from eight efforts overall.
Celta move to 15th, three points above the drop zone, while Zaragoza are a point and two places above.
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