Mbappe scored in each half and won a penalty that was converted by Fabinho to lift the principality team to 71 points from 30 games, six clear of second-placed Paris St Germain, who host Olympique Lyonnais later on Sunday.
The 18-year-old Mbappe scored the opener on Wednesday as Monaco beat Manchester City to advance into the quarter-finals of the Champions League, before receiving a maiden call up to the France squad for their World Cup qualifier against Luxembourg and a friendly against Spain later this month.
Mbappe opened the scoring after 13 minutes with a low left-footed shot that beat keeper Remy Vercoutre.
He was then brought down by Damien Da Silva as he raced into the area, and Fabinho converted the resulting penalty to put the visitors in the driving seat.
Mbappe was at it again nine minutes before fulltime when he scored his 12th league goal of the season with a fine header from Joao Moutinho's cross. It was his ninth in his last seven appearances.
"We know how to kill a game," said Mbappe.
Read the full article on eurosport.co.uk: Mbappe shines again as Monaco extend Ligue 1 lead