Russia headed into the curtainraiser at the 80,000-capacity Luzhniki, the crucible of Russian and Soviet sport, without a victory in over eight months and ranked a lowly 70th in the world.
Only South Africa, in 2010, have failed to advance from the group stage as the host nation and a seven-match winless run had ramped up the pressure on Stanislav Cherchesov's side.
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.
But his replacement, former Real Madrid winger Cheryshev, celebrated his recent recall to the national side with Russia's second goal two minutes before half-time. Cheryshev was still left with plenty of work to do inside the area after a pass from Roman Zobnin, brilliantly flicking the ball past two closing defenders before rifling into the roof of the net.
Saudi briefly threatened early in the second half when an inviting cross in from the right skipped just beyond the reach of Taiseer Al-Jassam.
The forward was soon replaced by Dzyuba, who struck almost immediately by heading another Golovin cross beyond a helpless Muaiouf in the 71st minute. Cheryshev hammered in a fourth with the outside of his left in stoppage time and Golovin capped a magnificent performance by bending in a last-gasp free-kick.
Russia meet Egypt in their next match on June 19 in Saint Petersburg, while Saudi Arabia will look to rebound against group favourites Rostov-on-Don a day later.
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