Estadio Balaidos has become something of a fortress of late for Celta, who have won four of their last five games there.
And though they went close on numerous occasions in the first half - notably when Charles hit the post just before half-time - they could not find a way past Athletic, who took their lead over fifth-placed Villarreal to four points.
Celta are unbeaten at home since November 9 and they showed their confidence as they dominated the chances in the first period.
Santi Mina was the first to try his luck but he pulled his shot wide from inside the area after 15 minutes, while Charles fired over six minutes later.
Just before the half-hour mark Rafinha brought a brilliant save out of Gorka Iraizoz as his left-foot strike from the edge of the box was turned over by the visiting goalkeeper.
And Celta went closer still two minutes before the break as Charles drilled a shot against the post from 18 yards.
The hosts could not keep up their onslaught after the break, although Augusto Fernandez had a chance which he fired off target.
As the half went on the visitors finally started to create opportunities, with first Iker Muniain and then Ibai Gomez failing to find the target with decent chances.
But with the final whistle approaching it was again Celta who looked the more likely to score and the final chance went to substitute Mario Bermejo, who headed over from close range.