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Although Barca ran out comfortable winners, it was Granada who had the game's first chance, but Youssef El Arabi flashed his effort over the bar.
The visitors defended stoutly until the 26th minute, when Hector Yuste gifted the ball to Neymar, whose deflected finish nestled in the back of the net as the home side went a goal ahead.
In the 43rd minute, Ivan Rakitic made it 2-0 with a strong header from Lionel Messi's centre and it became 3-0 on the stroke of half time when Neymar showed his predatory instincts to lash home a loose ball.
The game was already won by the time that the second half began, but it didn't prevent Barcelona from continuing to pour forward and Messi got in on the act in the 62nd minute with a header.
Messi then turned provider once more as he sent a sharp through-ball into Neymar, who completed his hat-trick with a composed finish inside the area.
There was still time for Messi to get his second goal of the night to go along with his two assists, as the Argentine weaved through the Granada defence before effortlessly planting a finish into the corner.
Barcelona saw out the final few minutes to gain another clean sheet as they held onto the impressive record of being the only La Liga side yet to concede a goal this season.