France starts their World Cup campaign on June 16 against Australia, before facing Peru and Denmark, while hosts Russian Federation open against Saudi Arabia on June 14, with Egypt and Uruguay also in their group.
But Mbappe put France into a 40th-minute lead when he latched onto Pogba's through ball, before cutting inside and lashing a low shot home despite the attention of two Russian defenders.
If United can cement a midfield built around Pogba and make it a success, the Reds have the potential to demolish teams.
Chelsea legend Didier Drogba has insisted the recent problems between Manchester United manager Jose Mourinho and the club star midfielder Paul Pogba are actually a sign of how highly the Portuguese coach rates the player.
He nearly had a second just three minutes later, Lunev doing well to keep out Mbappe's strike from point-blank range after a cutback supplied by Martial, who also had two optimistic penalty appeals dismissed.
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The midfielder scored superbly as well as providing an assist in the game.
Mbappe, however, made sure of France's victory when he slalomed through the defence and beat Lunyov again with another low shot.
The Paul Pogba that the world, and Manchester United fans, have been waiting for quite some time to see again showed up for France during the global Federation Internationale de Football Association break.
The Japanese used Standard Liege's stadium as their base for two warm-up games having snatched a last-gasp draw with Mali on Friday.
If the 19-year-old can carry on that sort of display and match up to Zidane's performances, France will be one of the favourites for the World Cup.