The Spaniard fired in a brilliant volley from the edge of the penalty area in the 88th minute to complete the hosts’ comeback.
Levante were in front at the break after Sergio Postigo put them ahead in first half stoppage time.
Athletic captain Iker Muniain equalised midway through the second half when he headed in Capas cross from close range.
With the Basque side pushing on in search of the winner, Capa swept a sweet volley into the bottom corner from outside the 18-yard box.
The win moves Athletic Club into sixth place in LaLiga Santander, while Levante stay in the bottom half.