Gazinsky put home a header, and the Saudi Arabian goalie simply couldn't get to it despite a good effort.
The first goal arrived after 12 minutes from a neat header by unheralded 28-year-old Yuri Gazinsky, and came from a pinpoint cross from Golovin, the CSKA Moscow midfielder, who has been linked with a host of top English Premier League clubs.
Number 70 Russian Federation and 67 Saudi Arabia kicked off the tournament as the lowest-ranked of all 32 teams after a short opening ceremony with Robbie Williams as headliner on an overcast evening.
It's the first time Russian Federation is hosting the World Cup.
But they will be aware that the Asian qualifiers look desperately ill-equipped to trouble Egypt or group favourites Uruguay, who meet tomorrow, and that there is still much to be done for the hosts to secure progress to the knockout stage.
In addition to installing toilet bowls and painting the prison bars, Navalny said cell blocks have been fitted with LCD screens for prisoners to watch World Cup matches.
The second half witnessed similar dominance from the home side.
Another substitute, Artem Dzyuba, made it 3-0 with about 20 minutes remaining, putting the game out of Saudi Arabia's reach.
Saudi Arabia captain Osama Hawsawi was on his guard against Golovin - and Argentine referee Nestor Pitana didn't bother to consult the video assistant despite Golovin's penalty appeal.
Six Saudi female teenagers slated to serve as their country's flag bearers at the World Cup's opening match in Moscow on Thursday will be replaced by Russians after their trip was cancelled due to "logistical circumstances", organisers said.
Russia's bench players had their day of glory.
The preparations of 2010 winners Spain are in tatters after coach Julen Lopetegui was sacked just two days before their opening game on Friday against Portugal.
Saudi Arabia also play Uruguay and Egypt in Group A.
Saudi Arabia had 60 percent of possession and played almost twice as many passes as their hosts, but were still blown away on opening day.
- Saudi Arabia have not won any of their last 11 games at the World Cup (W0 D2 L9).