Fernando Llorente had two chances early on for the hosts, but the striker was unable to find the target.
He fared better in the 35th minute when he gave his side the lead thanks to a powerful header.
Mallorca could have been awarded a penalty just before the break but the referee waved away the appeals when it looked like a Bilbao defender may have handled.
As the hosts asserted their dominance in the second half, Iker Muniain should have done better when he blasted his shot over from 12 yards.
The forward made no mistake on the hour as he planted his header past Juan Sanchez in the Mallorca goal.
Bilbao should have had a third in the final minutes, but the linesman wrongly flagged Oscar Des Marcos offside.