Falcao’s goal came with 12 minutes left at the Stade Saint-Symphorien, and the win makes it three in a row at the start of the new season for Leonardo Jardim’s reigning Ligue 1 champions.
It is also now 15 on the bounce going back to February as Monaco surpassed the previous mark of 14 in a row established by Laurent Blanc’s Bordeaux in 2009.
Mbappe had been left out of the squad completely amid intensifying speculation surrounding his future.
The 18-year-old, who was outstanding in the second half of last season as the principality club won the title and reached the semi-finals of the Champions League, wants to move to Paris Saint-Germain.
The capital club and Real Madrid are both reportedly ready to pay 180 million euros ($211 million) for his services as they look to team him up with Neymar and Edinson Cavani in attack.
The young French international had already been left on the bench for the duration of last weekend’s 4-1 win at Dijon when Falcao scored a hat-trick and the Colombian again made the difference here.
The match, preceded by a minute’s silence as a tribute to the victims of the terror attacks in Spain, had been heading towards a goalless draw until Falcao’s intervention.
Monaco had won 7-0 in Metz last season, their biggest ever away win in the top flight, while they also won 5-0 when the teams met at the Stade Louis II. Mbappe scored a hat-trick in that match.
Falcao and Rony Lopes tested the Metz goalkeeper Thomas Didillon in the first half but the game was still finely poised when Jardim sent on former Lyon winger Rachid Ghezzal for his Monaco debut midway through the second half.
Nolan Roux threatened for Metz on the counter-attack but it was the visitors who were the most threatening and Kamil Glik’s header from a corner was saved by Didillon before the winner arrived on 78 minutes.
Ghezzal lifted a great ball into the box for Falcao, whose first touch took him past the goalkeeper before he slotted in his fifth goal in three league games this season.
Monaco’s eighth straight away league win also left Metz still without a point to their name.
Lyon are hoping to maintain their perfect start to the campaign when they host Bordeaux on Saturday.
Neymar is set to make his home debut for Paris Saint-Germain against Toulouse on Sunday following his world record 222 million-euro move from Barcelona.
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