Putin was caught smugly shaking hands with Crown Prince Mohammed bin Salman after Russian Federation scored the first of three goals against Saudi Arabia.
Gazinsky put home a header, and the Saudi Arabian goalie simply couldn't get to it despite a good effort.
And the Saudi goalkeeper was beaten again in the fourth minute of stoppage-time, Golovin adding to his two assists with a curling free-kick that left brought the home fans to their feet once again. Russia's win was also the biggest in a World Cup opener in 84 years since Italy's 7-1 over the United States in 1934.
A lack of an attacking threat in recent outings was a primary concern for Russian Federation going into a group campaign in which they will also face Egypt and Uruguay.
Group B is underway at 3am when Morocco, fresh from missing out on hosting rights to the 2026 tournament and appearing at a World Cup for the first time since 1998, meet Iran, who are looking to progress to the knockout rounds for the first time ever.
Another substitute, Artem Dzyuba, made it 3-0 with about 20 minutes remaining, putting the game out of Saudi Arabia's reach.
Dzagoev pulled up with an injury midway through the first half and was substituted in the 24th minute.
The result equalled the best-ever in a World Cup opening game - Brazil beat Mexico 5-0 in Geneva in 1954 - as Russian Federation took full advantage of a Saudi team who's defending fell painfully short of World Cup standard, while their attack was non-existent.
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.
It's hard to imagine Russian Federation beating the vastly superior Uruguayans, but if they can get a draw with Egypt, whose best player, Mo Salah, is fresh off a serious shoulder injury suffered in the Champions League final, they could scramble through to the next round.
Hello, hello, four years of waiting is finally over and the much anticipated 2018 World Cup is here. "We are focused on the opening game, that will set the tone for the other games".
Coach Juan Antonio Pizzi had earlier said that Saudi Arabia would play without fear on Thursday.