Laporte rose highest in the area to nod Markel Susaeta's cross into the top left corner after just eight minutes.
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The hosts had a glorious chance to level things up on the stroke of half time when Carlos Gurpegi brought down Adrian Colunga inside the area, but Diego Castro saw his resulting spot kick saved by Gorka Iraizoz.
Susaeta almost doubled Bilbao's lead just two minutes after the restart, but his low strike from outside the box was well saved.
Ander Iturraspe was the next to come close for Bilbao, but once again Moya was on hand to deny the visitors.
Getafe couldn't find an equaliser in the closing stages as Bilbao leapfrogged the hosts into fifth place in La Liga.