Russian Federation took the lead on 31 minutes after New Zealand lost possession in their own half.
President Vladimir Putin, for whom the tournament and the World Cup are prestige projects, said Thursday: "Let us hope that the guys will try to perform well, like real fighters".
The former Russian worldwide goalkeeper has set his squad the ambitious task of winning the Confed Cup, a tournament that serves as a tune-up for next year's World Cup.
Fyodor Smolov both began and ended a counter-attack which put the result beyond doubt in the second half, with Russian Federation now turning their attention to a game against Portugal on Thursday. "And we've took the full-scale measures to assure the event's security".
Federation Internationale de Football Association secretary-general Fatma Samoura said that curbing problems now is "exactly the whole purpose" of anti-discrimination work at the World Cup rehearsal tournament.
"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.
Portugal manager Fernando Santos has suggested that he will rotate his squad through the group stages, with the final game in particular against New Zealand likely to see plenty of changes in personnel.
"The game didn't go how we wanted to go", New Zealand coach Anthony Hudson acknowledged.
The incidents sparked further fears about hooliganism at the Confederations Cup and the World Cup in 2018.