Russian Federation went ahead in the first half of the Group A encounter through what was credited as an own goal from the New Zealand defender Michael Boxall, and Smolov wrapped up the victory in the 69th minute.
In what was Russia's first ever appearance in the Confederations Cup, Stanislav Cherchesov's side will be happy with a strong showing in the opening match on Saturday.
Next year's World Cup will take place in 12 stadiums spread across 11 cities, including Moscow, St. Petersburg, Kazan and Sochi, the host cities for the Confederations Cup.
Putin this week demanded better results from the 63rd-ranked Russian Federation team and for the players to perform like warriors.
But weak defending allowed Russia's Fedor Smolov to slip past the New Zealand defence and tap in a low cross by team mate Alexander Samedov in the 69th minute.
"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.
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"He is concentrating on playing for the national team and he wants to give the motivation to have a good tournament".
The other two Group A teams include European champions Portugal spearheaded by the global superstar Cristiano Ronaldo and the most decorated CONCACAF team Mexico.
Midfielder Denis Glushakov flicked the ball over goalkeeper Stefan Marinovic in the 31st minute as New Zealand defenders rushed back to try to clear it off the line.
The Confederations Cup takes flight as hosts Russian Federation take on New Zealand in Group A play Saturday at 11:00 a.m. ET live on Telemundo Deportes. A three-player race to meet the rebound off a post saw the sliding Boxall's trailing right arm get the final touch in a bundle of bodies.
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.
A Confederations Cup trophy, never mind a World Cup title, might be too much to ask even for Putin, But Saturday was a start.
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