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Napoli doubled their lead when Mertens picked out Zapata in the box and he drove a left-footed shot into the bottom corner.
Rafael Benitez's side were in complete control of the game and duly scored their third of the evening when Callejon raided down the flank and crossed into the middle for Zapata, who headed home to get his second of the match.
Just before the break, Mertens tried to get a goal of his own as he launched an effort with a left-footed drive, but Andrade made a good stop to keep his shot out.
However, Mertens was not to be denied his goal and he added Napoli's fourth in the second half as he raced into the area and placed the ball past the keeper with a neat finish.
Mertens notched his second goal of the game when he collected a pass from Lorenzo Insigne and drove the ball past Andrade with a powerful right-footed strike to seal the win.