Gazinsky put home a header, and the Saudi Arabian goalie simply couldn't get to it despite a good effort. Gazinsky charged forward to meet the ball as Saudi player Taisir Al-Jassam stumbled, leaving a simple finish.
Russian President Vladimir Putin, Saudi Crown Prince Mohammad bin Salman Al Saud and Federation Internationale de Football Association president Gianni Infantino attended the opener along with further dignitaries and heads of state - but none from Western European or North American countries. Putin then reached over to shake the prince's hand.
The reaction after the first goal.
The hosts did better in the 43rd on another fast move, with the ball eventually falling to Cheryshev who rounded two defenders and smashed into the net at the near left post.
Russian Federation have provided injury updates to central-midfielder Alan Dzagoev who was forced off the pitch in their opening match of the World Cup against Saudi Arabia. "I already felt very happy when I knew I could come here with my squad, but I never, ever dreamed of something like this".
It also helps if you are facing a team who have now lost eight and drawn two of their last 10 World Cup matches, whose defending fell painfully short of World Cup standard and whose attack was non-existent. But that's not the case with Russian Federation, whose two remaining games are against group favorites Uruguay and Egypt.
Half an hour in the closing half both teams made replacements with Saudi Arabia switching Abdullah Otayf for Fahad Almuwallad and Russian Federation replaced Alexander Samedov with Daler Kuziaev. Egypt and Uruguay play Friday in Yekaterinburg.
Dzagoev pulled up with an injury midway through the first half and was substituted in the 24th minute.
On the day of the curtain-raiser, Russian Federation freed the main opposition figure to Putin, Alexei Navalny, from jail after he served a 30-day sentence for organising an illegal protest.
Yet given Saudi Arabia's high turnover of coaches, including a previous mid-World Cup sacking, the Argentine-born Pizzi could well be on his way before he gets a chance to try and rectify the situation.
With a maximum capacity of 80,000 spectators, the Luzhniki stadium in Moscow was the site of the opening ceremony and will also be the grounds for the final game, scheduled for July 15.