Dmitri Poloz set up the chance with a through ball to Denis Glushakov, who tried to chip All Whites goalkeeper Stefan Marinovic.
The Russians - who are hosting the tournament one year before they stage the World Cup - took the lead in the 31st minute.
(AP Photo/Dmitri Lovetsky). Russia's Denis Glushakov, center, scores the opening goal during the Confederations, Cup Group A soccer match between Russia and New Zealand, at the St.Petersburg stadium in St.Petersburg, Russia, Saturday, June 17, 2017.
An own goal from Kiwi defender Michael Boxall and Fyodor Smolov's second-half strike gave the hosts the flawless start to the campaign as they prepare to host the 2018 World Cup.
The hosts continued to crank up the pressure after the break, forcing the impressive Marinovic into a fantastic double save, but Russian pressure finally told when Krasnodar striker Smolov - top scorer in the Russia Premier League for the past two seasons - tapped home from an Aleksandr Samedov cross on 69 minutes.
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"Welcome to Russian Federation!" - inspired his players.
"We're a tight-knit team and we really understand all the different phases we have to go through: when it's time to train we train, and when it's time to kick back and relax we do that too".
"The first half was quite scrappy - I think certainly the first goal was preventable, we gave the ball away in a really bad area".
Pizzi says the Chile staff is "optimistic from the images we've seen, but we understand and know that the player still feels pain, and that's why we'll wait until tomorrow to decide if he plays".
Although New Zealand proved they could also be unsafe on a few occasions, Russian Federation clearly dominated the game from start to finish.
The FIFA 2018 World Cup will be held on June 14-July 15 2018 in the cities of Moscow, St Petersburg, Sochi, Kazan, Ekaterinburg, Kaliningrad, Nizhny Novgorod, Rostov-on-Don, Samara, Saransk, and Volgograd.