Celta, with 21 points, are 14th.
The hosts struggled to play out from their own end in the early going and the first three chances here on Monday in front of the 12,000 spectators at Vigo's Balaidos Stadium came on free-kicks.
With a focus on the counter-attack, Athletic's moment arrived in the 19th minute, when Iñaki Williams went almost the length of the pitch and got the ball to Iker Muniain in the area for the goal.
The contest then settled into torpor until the dying seconds of the first half, when 19-year-old Fran Beltran converted a corner to bring Celta level with his first LaLiga goal.
But the rally sputtered as the minutes passed and Athletic reclaimed the initiative, again with Williams in the vanguard.
Conceding a second time appeared to sap whatever remained of Celta's morale and the closest the hosts came to equalizing was a header by Gomez in the final play of the match.
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