Pogba's second spell at Manchester United hasn't gone as well as he or the club had hoped.
But France had the final say as Mbappe added his second, firing through the legs of Russian Federation stopper Lunev.
The game was preceded by a minute's silence to remember the 64 people, including 41 children, who were killed in a fire at a Siberian shopping centre on Sunday.
It took France 40 minutes to find the breakthrough, but Pogba's inch-perfect pass for Mbappe sent the PSG teenager racing through on goal, and he duly provided a relaxed finish.
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 worldwide Federation Internationale de Football Association break.
But he was recalled for this match, along with United teammate Anthony Martial.
Russian Federation pulled one back in the 68th minute, substitute Igor Smolnikov swinging in a brilliant low cross from the right flank that Smolov met at the back post to smash past Lloris.
Pogba, was left out of the starting line-up for last week's clash with Colombia.
Pogba made the first of Kylian Mbappe's two goals and added a 30-yard free-kick himself. "So close to the World Cup, questions are being asked as to why it wasn't dealt with as it occurred during play".
France kick off their World Cup campaign against Australia on June 16.