Russia 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.
Russia 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 -- top scorer in the Russian league last season -- wrapped up the points in the 69th minute.
It was the ideal start for the Russians in a game played at the new Krestovsky Stadium, where President Vladimir Putin and FIFA chief Gianni Infantino both gave speeches before kick-off.
Group A rivals Portugal, led by Cristiano Ronaldo, and Mexico meet in Kazan on Sunday, with Russia's next game against the Portuguese in Moscow on Wednesday.
This competition offers Russia a chance to showcase its readiness to host the 2018 World Cup amidst off-field concerns surrounding hooliganism and security.
But it is also an opportunity for coach Stanislav Cherchesov and his side to show what they can do on the pitch, although they will face far greater tests in their next two outings than what New Zealand provided here.
"I liked New Zealand's team but luckily we managed to cancel out their strengths and displayed ours, and that was the key to our win tonight," Cherchesov said.
The Krestovsky Stadium was late in opening and came home well over budget, while serious problems have been experienced with the playing surface.
But the venue, which will also host the final on July 2, came through this opening test unscathed, even if there was a considerable number of empty seats.
Cherchesov's men were too strong for a limited New Zealand side and were unlucky not to take an early lead, Viktor Vasin heading against the post from an Alexander Samedov corner, with Michael McGlinchey clearing off the line.
Dmitry Poloz then went down under a challenge from New Zealand goalkeeper Stefan Marinovic in the area, but the Colombian referee waved away the penalty appeals and there was no intervention from the video assistant.
Smolov had an effort ruled out for offside before the opening goal arrived just after the half-hour mark.
Alexander Yerokhin sparked the attack with an interception around 30 yards from goal, and his pass was helped on by Poloz into the path of Denis Glushakov.
The Spartak Moscow midfielder lifted the ball over Marinovic and saw his effort hit the post before Boxall, one of two defenders desperately scrambling back to try to clear, helped it over the line.
"I thought I scored the opening goal but it doesn't really matter who was credited for it," Glushakov said. "The main thing is that we took the lead.
"We can play much better and perform much more skilled football than we showed today and we made too many mistakes. That means we still have plenty of homework to do."
New Zealand's goalkeeper Marinovic, who plays in the German lower leagues, did well to keep the Oceania champions in the game in the second half, producing a fine double save from Poloz and Yerokhin and then turning away another effort from Rostov forward Poloz.
But Russia did increase their lead with just over 20 minutes left, Smolov finding Samedov on the right and then arriving unmarked in the box to convert his team-mate's cross.
"Obviously in the first game of the tournament we wanted to get a better result than we did," New Zealand manager Anthony Hudson said.
"So, we're slightly deflated but the team showed a lot of spirit."