Athletic had made a solid start to the season after flirting with relegation last term but they turned in an error-strewn performance devoid of inspiration at Granada's Estadio Nuevo Los Cármenes.
The Morocco international scored his second eight minutes later when Pape Diakhate flicked on a Diego Buonanotte corner and he headed past Athletic goalkeeper Gorka Iraizoz.
They were Granada's first goals at home in four matches this season and lifted them to 12th on eight points from seven games.
Bilbao stay fifth on 12 points.
"It's important to win at home and we put in a huge effort," Buonanotte told Spanish television broadcaster Cuatro. "It's all about building confidence and winning games."
Athletic midfielder Herrera said his side would have to improve their away form if they are to achieve their objective of qualifying for Europe.
Ernesto Valverde's side have won all three of their matches at their new San Mames stadium but have lost their last three on the road after an opening-day win at Real Valladolid.
"If we want to be up at the top of the table we have to perform away from home as well," he told Cuatro.
"There's no point in looking for excuses," he added. "We are a completely different team away from home and that's what we have to correct."
Champions Barcelona and Atletico Madrid are the only two teams with a perfect 21 points from their seven games.
Real Madrid are five points adrift of the leaders in third after losing 1-0 at home to Atletico on Saturday.