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.
Russian Federation opened their campaign in emphatic fashion, thrashing Saudi Arabia 5-0 in front of 78-thousand enraptured fans at Moscow's Luzhniki Arena.
Luzhniki exploded into raptures after only 12 minutes when Yury Gazinsky headed home for the opener.
Yuri Gazinskiy and Cheryshev struck first-half goals to open their worldwide accounts at Luzhniki Stadium, Artem Dzyuba adding a third 89 seconds after his introduction as a second-half replacement, but an injury to star man Alan Dzagoev will cause concern for Russian Federation. Golovin added the fifth from a free kick.
But they will be aware that the Asian qualifiers look desperately ill-equipped to trouble Egypt or group favourites Uruguay, who meet tomorrow, and that there is still much to be done for the hosts to secure progress to the knockout stage.
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.
Russian Federation lost Dzagoev to a hamstring injury midway through the first half, the CSKA Moscow midfielder clutching his hamstring as he crumpled to the turf.
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Russia's players were significantly taller and heavier than the Saudis, a help when challenging for the ball and when the penalty area was crowded.
Stanislav Cherchesov's side did not let Dzagoev's injury affect them and they scored the second goal their enterprising play deserved three minutes before the break.
Saudi Arabia's route to the knockout round is much more hard.
With a maximum capacity of 80,000 spectators, the Luzhniki stadium in Moscow was the site of the opening ceremony and will also be the grounds for the final game, scheduled for July 15.
The 2018 FIFA World Cup opening ceremony will have a slightly different format to previous editions of the tournament.
Victory for Russian Federation, ranked a lowly 70th in the world - three places below Saudi Arabia - was vital for the home nation's hopes of progressing, with tougher games against Egypt and Uruguay to come.
Saudi Arabia are led by coach Juan Antonio Pizzi, yet he faces an nearly impossible challenge of piecing together a team ready for World Cup action as most of his players are based in a domestic league that lacks quality.