Getafe dominated the opening minutes, getting behind Athletic's defense twice in the fourth minute, but it was Athletic which scored when Laporte rose to head in Markel Susaeta's corner.
''We had been giving signs of fragility up until now, but not this time,'' Athletic striker Ander Herrerea said. ''I won't predict how far up we can go because I think we should be prudent about what we aim for as the league is very long.''
Getafe had an opportunity to equalize when Adrian Colunga was fouled by Carlos Gurpegi and Mikel Balenziaga inside the penalty area in the 43rd, but goalkeeper Gorka Iraizoz saved Diego Castro's shot.
''The team didn't deserve to lose, a draw would have been a much fairer result,'' Castro said. ''I had scored every one of the last 15 penalties that I have taken. No one likes to fail a penalty.''
Iraizoz took a knock and was substituted by Iago Hereria for the second half.