Allan Nyom converted Dimitri Foulquier's cross inside the box eight minutes into the game, controlling the ball before finding the back of the net via the post to put the visitors - who had lost their last four games coming into this one - ahead.
The Nazaries managed to level up the contest before the interval, however, courtesy of Eneko Boveda's perfectly-placed shot into the top-left corner of the net, which left Roberto Fernandez with no chance.
Eibar wasted a big opportunity to take the lead shortly after when Federico Piovaccari failed to find the target after being picked out inside the area.
The best chance of the second half fell to Piovaccari once more, but he could not find a way to goal from close range.
The result means that Granada remain in 14th place, while Eibar climb to 12th.