Levante took the lead after a quarter of an hour when Iborra flicked a header past los Che stopper Vicente Guaita.
Valencia equalised through Brazilian midfielder Jonas after 27 minutes when he pounced on some indecision in the penalty area to thump past Gustavo Munua.
Soldado then gave his side the lead just before the break when he met a cross
from Joao Pereira before unleashing a volley past Munua.
The former Real Madrid man was at it again in the second half but this time his strike hit the crossbar with 15 minutes remaining.
With time running out for Juan Ignacio Martinez's side, Bakero grabbed an unlikely equaliser when he drove at the Valencia defence before curling an effort into the bottom corner with two minutes left.