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. New Zealand's Michael Boxall got a touch on the ball and was credited with an own goal.
Scoring chances came early for Russia, playing with confidence and unexpected flair, a powerful header by defender Viktor Vasin bouncing off the inside of the post before being cleared by New Zealand's Michael McGlinchey.
Marinovic kept his team in the match early in the second half with back-to-back saves, diving to punch away a header by Dmitry Poloz before scrambling to his left to smother a rebound attempt by Aleksandr Erokhin.
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.
World champions Germany and the champions from FIFA's six confederations are competing in the two-week tournament that will allow Russia to test its football infrastructure in four of the 11 cities hosting World Cup matches.
Russia, a record low 63rd in FIFA's world rankings, face Portugal on Wednesday and New Zealand play Mexico the same day.
(Reporting by Vladimir Soldatkin and Alexander Winning; Writing by Moscow newsroom, editing by Ed Osmond)
