Mexico now advances to play the host of the tournament, Russia, in the group finale on Saturday.
All Whites coach Anthony Hudson conceded the game was physical but suggested the competitive display of his unfancied team was behind the Mexicans' angry response to some incidents.
"Our talent can surprise them - and that can be the factor which can win us the match".
"We all have good memories of 2013", said Sanchez.
The Real Madrid star was unmarked at the back post, where he rose to head Raphael Guerreiro's cross past Russian Federation keeper Igor Akinfeev and into the net after just eight minutes.
Ronaldo proved the main threat throughout the first half as the hosts offered little going forward, and he tested Akinfeev with a 25th-minute free-kick before forcing the keeper to block with his legs seven minutes later.
Group rivals Mexico and New Zealand meet later in Sochi.
The Mexicans came out firing in the second half and should have leveled matters in the 49th minute but Giovani Dos Santos blazed over from close range. "Let's see. The exam results will tell us".
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Only a superb one-handed reflex save from Akinfeev, who made his 100th global appearance, stopped Andre Silva's bullet header just after the break.
Tensions erupted in the first half when Mexico coach Juan Carlos Osorio swore at the New Zealand coaching staff over an injury to Carlos Salcedo that medics later determined would rule the defender out of the rest of the tournament.
He said he was taking some of the blame for the loss. "I know the talent and ability of my players and we have the ability to face them".
Mexico's Confederation's Cup took a turn for the worse Tuesday, as Carlos Salcedo was taken off the field on a stretcher against New Zealand.
New Zealand coach Anthony Hudson had vowed they would bounce back after Saturday's opening 2-0 defeat by Russian Federation and his team were true to his word.
Mexico equalised when Aquino broke down the left flank and passed to Marco Fabian, who squared for forward Jimenez to fire home on 54 minutes.
Oribe Peralta completed Mexico's comeback in the 72nd minute to eliminate the Oceania champions with one game to spare.
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