Russian Federation made it 3-0 in the 71st minute when Golovin chipped in a cross for giant striker Dzyuba to rise and head in from close range.
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.
But, even more spectacularly, Cheryshev became the first ever substitute to score in the first half of a World Cup opener, a record the midfielder will no doubt welcome along with the three points he helped his country to win. The winger puts the ball in the top corner giving no chance to the Saudi keeper.
Despite the lack of expectations, the hosts were under pressure to perform in the opening match of the tournament and could have easily crumbled, but they held their nerve to produce a strong performance.
The host nation had the momentum towards the 20th minute and were unlucky not to have found the second goal through their high press.
A second-half substitute, it took Dyzuba just 89 seconds to get on the scoresheet against Saudi Arabia. Saudi failed to clear a corner, Aleksandr Golovin crossed, and Iury Gazinski guided a header into the far corner.
It's the end of the first half and it's the host nation who are now ahead in terms of goal.
Playing just his seventh game for Russia, Gazinsky set the ball rolling before Cheryshev opened his account in his 12th appearance.
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24th minute: Russia's Alan Dzagoev has to leave the game due to injury.
"The team have to come out and play", Akinfeev said after a 1-0 friendly loss to Austria last month in which Russian Federation managed no shots on target.
Halftime: Russia 2, Saudi Arabia 0.
Collecting a pass from Roman Zobnin on the left of the box he showed great composure to nonchalantly dink the ball inches above two prone defenders desperately sliding in, before lashing into the roof of the net.
But first, here are 12 incredible stats from the 2018 World Cup opener.
In the 35th minute, Golovin went down inside the box as Saudi defenders struggled to keep up with his pace and movement. Osama Hawsawi makes inch flawless tackle.
When Dzagoev limped out midway through the first half with what appeared to be a hamstring injury, Russia's hopes of achieving anything significant looked to be leaving the pitch with him.
The Russia v/s Saudi Arabia World Cup 2018 match will take place on Thursday, June 14, 2018.
Despite hopes being low going into the game, both sides put up a good attacking fight with Yury Gazinsky giving Russian Federation the lead after just 12 minutes and Villarreal midfielder Denis Cheryshev doubled their lead just before half-time.