Cheryshev added a fourth with a superb finish before Golovin curled in a superb free-kick in injury time as President Vladimir Putin watched on in delight.
The opening goal came soon after, as Saudi Arabia failed to clear a corner and a curling cross in from the left by Golovin picked out an unmarked Gazinsky to head low into the far corner.
The best player on the pitch, though, was central playmaker Aleksandr Golovin, who was rewarded for his offensive sparkle with a wonderful goal from a free kick just before the final whistle to cap off the scoring. It is the first time that a substitute has scored in the opening game of a Fifa World Cup competition.
Both sides tried to assert their dominance in the opening exchanges by holding onto the ball and dictating the tempo of the game.
Russian Federation had a penalty appeal turned down in the 35th minute, but Saudi captain Osama Hawsawi got enough on the ball when he challenged Golovin to avoid censure from VAR.
Kim Kardashian West Visits Alice Johnson In Southaven
Later, when Kardashian West called with the clemency news, Johnson said she "went into a full-fledged, Pentecostal holy dance". Despite being locked away for what Johnson thought would be the rest of her life, she told Hoda she never gave up.
Women in Saudi Arabia were allowed to attend soccer matches for the first time this year, as the deeply conservative Muslim country takes steps to ease some restrictions on them. They inexplicably sacked Bert van Marwijk despite a successful campaign and then his successor Edgardo Bauza before the World Cup draw in November.
Putin hopes the most-watched event on the planet provides Russian Federation with the "soft power" needed to capture a sceptical world's hearts and minds.
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.
The final two goals came from the two stars of the show for Russian Federation.
The goal was exactly the start that Russian Federation needed to get the crowd going, and Luznhiki Stadium was rocking after Russian Federation won 5-0.
But if past history is anything to go by, Pizzi could well become the next coaching casualty of this tournament if Saudi authorities react with the emotive anger displayed in the past.