Iury Gazinsky scored after 12 minutes and Cheryshev added a second before the break after coming on as an injury replacement for Alan Dzagoev.
Artem Dzuyba netted a third before terrific late efforts from Cheryshev and Aleksandr Golovin wrapped up Russia's first win since October to launch their Group A campaign in style
Thousands of Russian and foreign fans had turned out to watch the World Cup opener in a Moscow fan zone.
A crowd of some 10,000 people, including many families with young children, crowded onto the hill above the stadium with giant screens set up to watch the game. Flag-waving supporters from all over the world let out huge cheers and chanted "Russia!" as the host team scored twice in the first half at the city's Luzhniki Stadium.
Russian fans were less numerous than international ones, but they were rooting for their team to pull off a triumphant start to the championship.
"I keep hearing so much bad stuff about our team but somehow I knew things would be ok, especially against the Saudis," said Igor Antonov, a 40-year-old school teacher.
There was a distinct South American flavour to the fan zone and exuberant supporters from Peru, Mexico and Colombia held competitive chant-offs, while cheering for Russia during the game.
"We were a bit worried that Russians will be cold because we South American people are very warm. But everyone has been so friendly," said Gabriela Chang, a 29-year-old Peruvian fan.
Tom Briskie, a 26-year-old Australian from Brisbane, admitted: "We were a bit worried before coming here because of all the media reports but it wasn't enough to put us off. "I totally didn't expect Moscow to be so nice," he added.
Michael Loffler, a 36-year-old German IT specialist who lives in Ukraine, was draped in both Russian and German flags.
"I came here to show that we (Europe and Russia) can be friends," he said.
There was some drama in the prelude to kick-off as Russia's behaviour – from charges of racism and hooliganism to a foreign policy sharply at odds with the West – was exposed and scrutinised.
Britain and some eastern European states still haunted by the Soviet era tried to organise a diplomatic boycott over the poisoning in England of Sergei Skripal, a former Russian spy, and his daughter.
While neither the British royal family nor British government members will attend, a wider boycott effort fizzled out. Russian organisers said they expected more than 20 heads of state to attend the opening match.
"We would like to underscore the validity of the FIFA principle of sport being outside politics," Putin told a meeting Wednesday of football's governing body FIFA.
"Russia has always adhered to this principle," he added. Putin is hoping the most watched event on the planet will help Russia capture the world's hearts and minds.
"Our goal is to make everyone, from football stars to ordinary fans, feel the good will and hospitality of our people ... so that they want to come back here again," he said. Russia spent more €11 billion on its most important event since the 1980 Moscow Summer Olympics.
The tournament is also a chance to project Russia as a global player that is accepted and respected even while being at odds with many in the West.
Russia is pulling it all off while bearing the brunt of international sanctions that began after it invaded and annexed Ukraine's Crimea in 2014.
Moscow's military backing of Bashar al-Assad's regime in Syria and alleged meddling in the 2016 US election only deepened its worst rift with the West since the Cold War.
But Russia's troubles don’t end at geopolitics. The bloody beating English fans took from Russian thugs at Euro 2016 in France has plagued preparations as much as any diplomatic dispute.
Security services either locked up or checked in on hundreds of neo-Nazi hooligans to make sure they do nothing to tarnish Russia's image.
Russia refused to issue tickets to nearly 500 of its supporters with suspected football underworld ties, while England has forced over 1,00