With the tie at 1-1 after the first leg, Barca rested Lionel Messi, Luis Suarez and Neymar but still had way too much for their opponents.
Lucas Digne broke the deadlock before Ivan Rakitic's penalty and a Rafinha strike put Barca firmly in control.
Turan's treble came in the second half, along with a Paco Alcacer header.
The Turkish midfielder's first was a stooping header from close range, with his second a powerful finish into the roof of the net after Alcacer's header had been saved.
His third was the best of the lot - a superb curling finish into the top corner after Hercules had failed to properly clear a corner.
Arguably the biggest cheer of the night, though, was reserved for the goal of Alcacer, who joined the club from Valencia in the summer for £25m but had failed to find the net in 12 previous appearances for his new club.
He could not miss from two yards out after Rafinha's cross had deflected his way.
It was ultimately the one-sided scoreline many had predicted but is a little harsh on Hercules, who claimed an impressive home draw in the first leg and frustrated Barca for over half an hour in the Nou Camp.
However, once Digne had poked in the opener and Rakitic had scored from the spot - following Fernando Roman's foul on Turan - Luis Tevenet's side were exposed allowing Barca to take full advantage.
Arda Turan scored a hat-trick as Barcelona claimed an emphatic win over third-tier Hercules to book their place in the last 16 of the Copa del Rey.