This is the first time in World Cup history that two substitutes have scored in the opening game of the tournament.
Saudi Arabia were continuing to give possession away easily and, from another concession dangerously close to their own area, Golovin fired over.
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.
"Even if we lose, we'll bring home political, economical and negotiating potential, " the crown prince said.
World Cup hosts have never lost their openers in 20 previous editions, and Russian Federation coach Stanislav Cherchesov would gladly accept a repeat of the 6-1 win in his only World Cup appearance when he kept goal for his country against Cameroon in 1994.
Saudi team are coming off the back of successive friendly losses to Italy, Peru and Germany, though they showed patches of encouraging form and did beat Algeria and Greece in May.
And the hosts struck after 12 minutes when they forced another corner which was half-cleared and, when Roman Zobnin crossed, Gazinsky headed home the tournament's opening goal.
It was a goal that prompted Russian President Vladimir Putin to turn to the Saudi crown prince Mohammed bin Salman, seated alongside Federation Internationale de Football Association chief Gianni Infantino, and shake his hand. "We are definitely extremely happy that we have managed everything".
Saudi Arabia - Al-Mayoof; Al-Burayk, Osama Hawsawi, Omar Hawsawi, Shahrani; Ateef, Faraj; Dawsari, Jassam, Shehri; Muwallad.
Sadly, the rankings also suggested it would not be high on quality, as Russian Federation came into the tournament as the lowest-ranked hosts in history, at 70th.More news: The Duchess of Sussex and the Queen arrive in Cheshire
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GOAL! 43rd minute: Substitute Denis Cheryshev gets his name on the scoring sheet doubling his teams lead.
In Group A, which also comprises two-time champions Uruguay and African hopefuls Egypt, the world No. 70 Sbornaya - "the team" in Russian - have to capitalise on a meeting against a side ranked just three rungs above them.
Russian Federation looked lively from the start as they poured into the vast spaces on both flanks and it was no surprise when they opened the scoring after 12 minutes as Gazinsky was totally unmarked to nod home Golovin's deep left-wing cross.
But there was a major blow for the hosts mid-way through the half as star playmaker Dzagoev limped off with a hamstring injury, to be replaced by Cheryshev.
With 43 minutes on the clock, the 27-year-old doubled Russia's lead with a blistering left-footer from inside the box.
Saudi Arabia's route to the knockout round is much more hard.
"I have never done anything like this", Cheryshev said.
The Green Falcons too are not in the best of forms but still looks much better when compared to their opponents Russian Federation.
"It all happened very quickly, the pass was a little bit too short so I did what I had to do, the defenders slid and I just tried to score", Cheryshev explained. "As for our strategy, we must change", Pizzi closed.