Russia's president was in the $750 million new stadium in his native St. Petersburg to see forward Fyodor Smolov's 69th minute goal add to an own goal by New Zealand defender Michael Boxall in the 31st.
New Zealand, meanwhile, were finding it tough to hold maintain possession of the ball, which led to a lack of chances.
Russian Federation sealed all three points as Smolov started and finished a swift passing move in the 69th minute to extended their unbeaten streak to four matches under Cherchesov.
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.
New Zealand nearly clawed themselves back in the game twice - first Ryan Thomas had a brilliant effort saved by Igor Akinfeev and then Tommy Smith had a powerful header cleared off the line by Yuri Zhirkov.
The All Whites did look livelier in the closing stages, but Russian Federation managed to hold out to keep the clean sheet.
"Obviously in the first game of the tournament we wanted to get a better result than we did", New Zealand manager Anthony Hudson said.
However, Russia's Federal Security Service (FSB) said last week terrorism did not pose any threat to Confederations Cup participants and spectators.
L'Arabie saoudite va lancer un bouquet pour concurrencer beIN Sports
Mais avec la reprise des championnats cinq autres chaines seront lancées avant d'atteindre les 11 prévues. Le compte à rebours a commencé pour le lancement du bouquet Pbs Sports .
"The fact the leader of the country came to the match is on the one hand an additional positive, but it is also an additional responsibility", Russian Federation manager Stanislav Cherchesov said.
The European champions will open the Group A program on Sunday against Mexico in Kazan.
"The match really required us to do something to score a goal and he's the right player for that".
Portugal's Cristiano Ronaldo and Mexico's Carlos Vela jump for the ball during the Confederations Cup, Group A soccer match between Portugal and Mexico, at the Kazan Arena, Russia, Sunday, June 18, 2017.
Madrid sports media is awash with headlines suggesting Ronaldo wants out.
A Confederations Cup trophy, never mind a World Cup title, might be too much to ask even for Putin, But Saturday was a start.
The competition hosts pressed forward from the outset, forcing the All Whites to clear two attempts off the line in quick succession, while a penalty shout was denied and a goal was ruled out for offside all before the half-hour.
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