Three of the previous nine Confederations Cups have been won by the host nation and Russian Federation, playing in the tournament for the first time, impressed with victory in Saint Petersburg.
New Zealand is now without a win in four trips to the Confederations Cup, and next plays Mexico on Wednesday in Sochi.
Chile's star player Arturo Vidal fiercely argued with referee Damir Skomina when a goal scored in first-half stoppage time by Eduardo Vargas was overruled nearly one minute later. The win puts them top of Group A, with Mexico and Portugal - the other two teams in the section - due to face off on Sunday.
Rating chances came early for Russian Federation, having fun with self-confidence as well as unanticipated panache, a powerful header by protector Viktor Vasin jumping off the inside of the article prior to being cleared by New Zealand's Michael McGlinchey. Tommy Smith then tidied up when Poloz poked a close-range shot slowly past Marinovic.
On Saturday, Russia marched on toward hosting football's biggest party when the rehearsal tournament, the Confederations Cup, kicked off in the $750 million new stadium in Putin's native St. Petersburg.
Poloz's neat touch set up Denis Glushakov, who dinked his effort over goalkeeper Stefan Marinovic and off the post before Boxall bundled the ball into his own net.More news: A boy and a girl for Beyonce and Jay Z?
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Russian Federation made a rapid start, with Aleksandr Golovin having a drive unconvincingly dealt with by New Zealand goalkeeper Stefan Marinovic, before the hosts were twice denied by goal-line clearances.
Ten minutes before kickoff, both teams lined up in front of the main stand to listen speeches by Putin and FIFA President Gianni Infantino.
"When the president of our country comes out to make a speech it mobilises us and gives us great motivation, but it also adds to our responsibilities", he said after the match.
"The game didn't go how we wanted", he said afterwards.
Russian Federation have implemented the special Fan ID, which allows visiting fans to enter the country without a visa and supporters to move freely between host cities for the duration of the tournament.