Cheryshev, who himself suffered an injury-plagued season, doubled Russia's lead 20 minutes later with a skill that left two Saudi players on the ground, and an emphatic left-foot shot into the roof of the net.
The 2018 World Cup kicked off on Thursday with the opening match between Russian Federation and Saudi Arabia.
This sustained pressure rewarded Russian Federation with an early goal as attacker Yuri Gazinsky got on the end of an inch-perfect cross to guide his headed effort past the Saudi goalkeeper.
Just a few moments later, Golovin curved a free kick over the Saudi wall and past goalkeeper Abdullah Al-Mayouf.
It was the host nation's first World Cup win since 2002, and it raises the hope that Russian Federation can get past the group stage for the first time since the Soviet era.
The World Cup kicks off in Russian Federation on Thursday as years of preparations dogged by diplomatic scandals give way to a month-long feast of action on the field.
Several minutes later Russia's Head Coach Cherchesov opted for another replacement and sent in Artyom Dzyuba in place of Fyodor Smolov.
With Dzagoev's injury, Denis Cheryshev was brought into the match with the hope of boosting Russia's chances of finishing the match against Saudia Arabia with the best possible outcome.
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. The CSKA Moscow playmaker was fantastic through, laying on two assists with pinpoint crosses either side of half time.
Saudi Arabia captain Osama Hawsawi was on his guard against Golovin - and Argentine referee Nestor Pitana didn't bother to consult the video assistant despite Golovin's penalty appeal.
Saudi Arabia had 60 percent of possession and played almost twice as many passes as their hosts, but were still blown away on opening day. "We are focused on the opening game, that will set the tone for the other games".
Brazil and their superstar Neymar are seeking a sixth global crown while Germany, who won their fourth World Cup in Brazil four years ago, will be determined to draw level with the Brazilians when the final is played in Moscow on July 15.
World Cup odds and matchups for opening week of action
Russian Federation were 1-0 up at the time of Dzagoev's injury after Yuri Gazinsky headed the hosts in front after 12 minutes. Russia's win was also the biggest in a World Cup opener in 84 years since Italy's 7-1 over the United States in 1934.
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