The hosts' unbeaten home record at San Mames appeared to be under threat when relegation-threatened Valladolid took the lead through winger Oscar's 15th-minute effort.
However, Ernesto Valverde's men quickly turned things around after half-time with four second-half goals that sealed a 12th win of the season for Bilbao.
Ibai levelled matters for Bilbao on 65 minutes, before substitute Oscar de Marcos put them in front 10 minutes later.
And the points were all but secured eight minutes from time, with Ibai finding the net for a second time as the forward took his tally for the season to six goals.
Ander Herrera added a fourth to compound Valladolid's misery on 86 minutes, although Valdet Rama did net a late consolation for the strugglers one minute into added time.
The result leave fourth-placed Bilbao two points ahead of Villarreal in the race for the final UEFA Champions League place, while Valladolid remain three points adrift of safety.
