Ricardo Gareca said Peru's 1-0 win against 10-man Venezuela was fully deserved.
Veteran striker Claudio Pizarro scored the decisive goal with 18 minutes remaining as Peru capitalised on their numerical advantage following Fernando Amorebieta's 29th-minute red card on Thursday.
Pizarro's 20th international goal blew Group C wide open, with Peru, Venezuela, Brazil and Colombia all level on three points and vying for a spot in the quarter-finals heading into final round of group-stage fixtures.
"It's always important to win. We had to win the match and we won," Gareca told reporters after notching his first victory as Peru boss at the fourth time of asking, having taken the reins in February.
"We knew it would be so contested. Venezuela is intense and it was hard. In the beginning they had the initiative, but when they were left with 10 players we learned to use it [numerical advantage].
"We had the advantage in terms of ball possession but not as to the situations. But in a tough game, we won deservedly.
"The dressing room is good. We know we have not achieved anything yet, but a win always adds confidence."
Peru face Colombia in their final group match on Sunday.
