The Paris Saint-Germain forward scored his 72nd and 73rd goals for his country to close on Pele's record of 77 for Brazil.
Neymar also upstaged South Korean captain Son Heung-min, the joint Premier League Golden Boot winner, who was kept quiet by a rampant Brazil at a packed Seoul World Cup Stadium.
Neymar's status for the match had been up in the air after he suffered a right foot injury during training on Wednesday, but he was the star of the show on a night when Richarlison, Philippe Coutinho and Gabriel Jesus all scored.
Brazil, ranked number one in the FIFA rankings, fielded a strong side and looked dangerous almost from the opening seconds with a header by Thiago Silva wiped out by an offside call.
Brazil took advantage of poor South Korean defending to take the lead on seven minutes.
Alex Sandro was left open as he charged into the left side of the box and he set up Fred for a shot from close range. The Manchester United midfielder misfired, but the ball took a fortuitous bounce to Richarlison, whose scrappy effort deflected in off goalkeeper Kim Seung-gyu.
Bordeaux forward Hwang Ui-jo levelled the score for the hosts on the half-hour mark, turning and firing it in off the left post with a smart finish.
But that goal came against the run of play and Brazil went ahead again on 42 minutes.
South Korean defender Lee Yong was called for a foul on Sandro inside the box and after a video review Neymar stepped up, calmly putting his penalty to the left of goalkeeper Kim.
Neymar scored his second penalty on 57 minutes, once again rolling the ball to Kim's left, before Coutinho and Jesus added gloss to the scoreline with two well-taken strikes.
Brazil will next play Japan in Tokyo on Monday, while South Korea host Chile on the same day.
Prior to the match, Tottenham's Son was awarded South Korea's highest sporting honour, the Cheongnyong Medal, by President Yoon Suk-yeol.