The Brazilian also weighed in with two assists in a virtuoso display which steals the headlines despite Edinson Cavani equalling the club's all-time goalscoring record with his 156th PSG goal.
The game was a breeze for PSG and they got off to a rampant start as Angel Di Maria opened the scoring with five minutes.
The former Barcelona player, who also set up two goals, was booed when he took the penalty as Cavani would have broken the club scoring record had he taken and converted it.
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Neymar did not manage to get on the scoresheet himself until three minutes before half time, but his opening goal was well worth the wait as he floated a free kick over the wall and into the top corner from 25 yards, leaving the keeper rooted to the spot.
Just to rub salt into the wound, Neymar buried a penalty past Reynet in the 83rd minute.
This season the world's most expensive footballer had bagged 11 goals in 14 games, which was a pretty decent record, but then he came up against Dijon on Wednesday night and proved he really could cut the mustard.
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Translations of the book in different languages such as Spanish, Arabic, Japanese, French, and German are also coming. The publisher also sold hundreds of thousands of copies in audiobook and e-book forms.
Neymar and Cavani have previously clashed over penalty taking duties, when the Uruguayan claimed a penalty ahead of Neymar against Lyon, and missed.
Neymar marked his return from a rib injury with the hosts' fourth goal just before half-time, and the Brazil worldwide made it a hat-trick with two more second-half strikes as Dijon were mercilessly ripped apart. The Brazilian was at hit again in the 73rd, slaloming past six Dijon players before finding the back of the net with a powerful shot from just inside the box.
PSG have 56 points and lead second-placed Olympique Lyonnais, who won 2-0 at En Avan Guingamp earlier, by 11 points.
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Since joining PSG, Neymar has scored 24 goals and assisted a further 16 strikes in 23 games.