Cheryshev scored a stunning goal with the outside of his left foot in time added on and Golovin sealed the rout with a goal direct from a free-kick.
Russia's first-ever FIFA World Cup will get underway at 6:00 p.m. local time (15:00 GMT) later on Thursday with the match between the hosts and Saudi Arabia at Moscow's 81,000-seater Luzhniki Stadium.
Yuri Gazinsky initially put Russian Federation ahead with a header from Alexander Golovin's cross when the Saudis failed to clear a corner in the 12th minute.
Denis Cheryshev showed great skill of his own to double the hosts' lead just before half time with a left-footed piledriver, and Artem Dzyuba headed Russia's third in the 71st minute - 89 seconds after coming on as a substitute. He walked free on Thursday, the day the Russian national football team kicks off the month-long tournament against Saudi Arabia in Moscow.
In a World Cup first, the video assistant referee system was available for the match between the tournament's lowest-ranked teams, though it wasn't used for an official review.
Both sides tried to assert their dominance in the opening exchanges by holding onto the ball and dictating the tempo of the game.
"There are so many unpredictable things in the World Cup".
Sara, another fan, praised the fact that the Saudi team had qualified for the World Cup at all - and wished the team the best of luck in future.
Russia, placed in Group A, is playing its next Group stage match against Egypt on June 19 in St. Petersburg, while Saudi Arabia is facing Uruguay on June 20 in the city of Rostov-on-Don.
Half an hour in the closing half both teams made replacements with Saudi Arabia switching Abdullah Otayf for Fahad Almuwallad and Russian Federation replaced Alexander Samedov with Daler Kuziaev.
Russian Federation dominated in front of a sell-out crowd of 78,011 - and millions more on TV - at Moscow's Luzhniki Stadium and also overcame a major blow when forward Alan Dzagoev had to limp off midway through the first half with what appeared to be left hamstring injury.
We have entered Federation Internationale de Football Association, so that is a big achievement for Saudi Arabia.
The World Cup favourites enter the fray this weekend.
Egypt's coach said prolific striker Mohamed Salah is "almost 100 percent" to play in their opening match against Uruguay on Friday after he had intensive treatment on the shoulder injury he suffered playing for Liverpool against Real Madrid in the Champions League final.