Ronaldo's eighth-minute header in Moscow gave Portugal their first win in the tournament and victory over New Zealand on Saturday would secure a semifinal spot.
Goals from Peralta and Raul Jimenez saw Mexico move top of Group A later in the day, above Portugal on goals scored, and knock New Zealand out of the competition.
Ronaldo let his football do the talking after the recent tax-evasion accusations that have left his Real Madrid future uncertain, with his second man-of-the-match performance following Sunday's 2-2 draw with Mexico.
The forward said Portugal were worthy winners after surviving a second-half Russian fight-back.
