The hosts won for the first time since the opening game of the season to move into mid-table.
Moroccan forward El-Arabi broke the deadlock with a penalty early in the second half and headed a second from close range to seal the points.
Victory would have sent Athletic into the top four, while going into the game the hosts had not managed a goal in September.
And they drew another blank in an uneventful first half.
Diego Buonanotte had a shot from 12 yards tipped over the bar by Gorka Iraizoz as Granada carved out the contest's first clear opening.
But Iraizoz's opposite number Roberto Fernandez had to be alert too as he produced a smart stop to keep out Ibai Gomez's effort.
The home goalkeeper was tested again on the stroke of half-time as he held Markel Susaeta's shot.
The hosts finally ended their drought seven minutes into the second half.
Ander Herrera, the highly-rated midfielder, fouled Yacine Brahimi in the area and El Arabi stepped up to place the penalty into the bottom right corner.
The hosts made it two in the 61st minute when Pape Diakhate headed on Buonanotte's corner from the left and El Arabi nodded home.
Granada almost grabbed a killer third, and El Arabi a hat-trick, minutes later, but his shot from the right side of the area was tipped round a post by Iraizoz.
Athletic never really threatened to get back into the match, with Gaizka Toquero's header which went wide the closest they came to getting a goal back.