Both sides had a host of opportunities in an enthralling first period, but it was Bilbao that took the lead on the stroke of the interval courtesy of a fine finish from Oscar de Marcos.
It was Celta that forced the issue in the second half, but they had to wait until the 84th minute to level the scores, with Iago Aspas finding the bottom corner from a tight angle.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
CELTA: Varas; Bellvis, Tunez, Johny, Oubina; Fernandez, Vila, Lopez, Madinda; Krohn-Dehli, Aspas
BILBAO: Iraizoz; Iraola, San Jose, Aurtenetxe, Ekiza; Gurpegi, Iturraspe, Susaeta, Muniain; De Marcos, Aduriz