Fyodor Smolov who was outstanding in the game got the second goal in the 69th minute.
On Sunday, Portugal and Mexico face off from Group A while Chile and Cameroon are playing each other from Group B. Shprygin said he had been notified by Confederations Cup organisers that his fan-ID - required to attend matches - had been cancelled.
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.
There's heavy pressure on Russian Federation to perform at the Confederations Cup, and with a slew of dignitaries in attendance on Saturday, the home team delivered.
"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. Federation Internationale de Football Association president Gianni Infantino opened the tournament with a speech inside the St Petersburg Stadium, with Russian president Vladimir Putin and legendary Brazil footballer Pele in attendance.More news: Trump again lashes out at Russian Federation probe, says he is being investigated
But we're a great side too, and I'm sure we can stop him.
The FIFA chief spoke before delegates of the Russian Football Union (RFU) in St. Petersburg.
"For us it is very important to make people in the country fall in love with the national team", said Smolov, the 27-year-old FC Krasnodar forward who was named the game's best player.
New Zealand is now without a win in four trips to the Confederations Cup, and next plays Mexico on Wednesday in Sochi.
Playing in the tournament for the first time, Russian Federation were on the front foot and had two early chances cleared off the line in the opening 10 minutes.
Russia's victory showed it can win a big game at home, even if Putin is in the arena.