Then, soon after the break, Pogba curled home a lovely free-kick from all of 30 yards.
With CSKA and Spartak defenders Viktor Vasin and Georgi Dzhikiya out with injuries as well as Zenit's forward Alexander Kokorin, Russia will likely once again depend on Fyodor Smolov up front.
Pogba doubled the advantage four minutes after the break with a curler into the bottom corner past the diving Andrei Lunev.
Mbappe put France into a 40th-minute lead when he latched on to Pogba's through ball, cut inside and lashed in a low shot.
It would be an ideal time for the central midfielder to regain form, with Manchester United looking to finish on a high after a disappointing European campaign while France will certainly need their playmaker come Russian Federation this summer.More news: Turkey's Erdogan: EU membership remains strategic goal
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Zenit were ordered by UEFA a year ago to partially close their stadium after fans displayed a banner praising former Bosnian Serb military leader Ratko Mladic, a convicted war criminal, during a 2-1 home win over Macedonian side Vardar Skopje also in the Europa League. "We need to analyse our performance quietly".
"It was heated between us a few times, but Jose will never attack people he doesn't like,"Drogba told Telefoot".
"So close to the World Cup, questions are being asked as to why it wasn't dealt with as it occurred during play".