Mbappe opened the scoring in the seventh minute when he met Falcao's knock-down with a low shot from inside the box, before the Colombia international finished at the near post after being picked out by Almamy Toure three minutes later.
Eighteen-year-old Mbappe beat the offside trap and slammed home past Thomas Didillon in the 20th minute for Monaco's third and then became the youngest player to score a Ligue 1 hat-trick since 2005 five minutes after halftime when he again evaded the Metz backline and finished delightfully.
Mbappe's pace and eye for goal were devastating for Metz and Falcao showed his enduring quality five minutes later when he met Benjamin Mendy's fine cross for Monaco's fifth, completing a miserable evening for the visitors.
"I congratulated Mbappe for his three goals and for all of his work, defensively as much as offensively," Monaco coach Leonardo Jardim told reporters.
"We played well. We created a lot of chances in the first half and the team now have to rest before we begin preparation for Bastia in two days."
Paris St Germain's 3-0 victory at Bordeaux on Friday had provisionally drawn them level at the top with Monaco, who then moved up to 58 points with victory.
Fourth-placed Olympique Lyonnais's indifferent form continued as they were beaten 2-1 away at Guingamp with goals from Moustapha Diallo and Nicolas Benezet cancelling out Alexandre Lacazette's opener.
Surprise package Nice, in third, can move three points behind the leaders -- and consolidate the final Champions League qualifying position -- if they win at Stade Rennes on Sunday.
(Reporting by Ed Dove; Editing by Toby Davis)
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