The hosts went ahead just before the half-hour mark when Rafinha pounced on a loose ball inside the box before finishing from close range.
Celta nearly doubled their lead just eight minutes later when Alex Lopez beat the offside trap before advancing into the Granada box, but his low effort could only clip the outside of the post.
The hosts should have killed the game just after the break when they had two chances in three minutes.
First Lopez blazed a close-range shot over the bar and then Charles scooped an effort over the frame of the goal just moments later.
Celta nearly went back in front just seven minutes later when Lopez made his way into box before slamming a low shot against the post.