Russian Federation went ahead in the first half of the Group A encounter through what was credited as an own goal from New Zealand defender Michael Boxall, and Smolov wrapped up the victory in the 69th minute.
Russia, a record low 63rd in FIFA's world rankings, face Portugal on Wednesday while New Zealand play Mexico the same day.
This competition offers Russian Federation a chance to showcase its readiness to host the 2018 World Cup amidst off-field concerns surrounding hooliganism and security.
KAZINFORM The main annual global football tournament among national teams - the FIFA Confederations Cup - kicks off in Russian Federation on June 17, Kazinform has learnt from TASS. "He is an idol, even for us players", admitted veteran defender Bruno Alves, the 35-year-old who has just signed for Scottish club Rangers.
However, the Socceroos have arrived in Russian Federation on the back of a narrow 3-2 World Cup qualifying win over Saudi Arabia earlier this month despite a 4-0 hammering by Brazil in a friendly in Melbourne.
A new pitch had to be hastily laid before kick-off after uprooted chunks of grass and bare spots on the field spoiled the first match held at the new venue in April.
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The first warning sign for New Zealand came in the seventh minute when Michael McGlinchley was forced to hack off the line after Viktor Vasin's header came back off the inside of the post.
But this ID also serves as an additional security measure as fans can not enter the stadium without it even if they have a ticket for the match.
Hudson acknowledged his team had "obviously" wanted a better result but was doing his best to remain upbeat ahead of their game against Mexico in Sochi in four days time.
The Portuguese sports daily A Bola published a front-page story Friday saying that Ronaldo was upset with the accusations made against him and that his decision to leave Madrid was "irreversible".
The match in Kazan will start will be followed by the Group B opener between African champions Cameroon and Chile in Moscow.
It is never wise to disobey Vladimir Putin and Russia's players ensured his midweek warning was not ignored as they kicked off the Confederations Cup in style, beating New Zealand with a performance far more emphatic than the 2-0 scoreline suggested.