Midfielder Christian Cueva missed a first-half penalty for Peru, skying it high over the bar, but Peru would miss many more chances in the second period, frustrated by some Schmeichel heroics and its own lack of composure in front of goal.
Despite Braithwaite's assertion that his team didn't play well enough on the night, they demonstrated enough to provide headaches for Bert van Marwijk and his Australian team.
Denmark join France on three points in Group C after Les Bleus registered a 2-1 triumph over Australia earlier on Saturday.
Ricardo Gareca opted to introduce Peru's record goalscorer Paolo Guerrero and the veteran nearly made an instant impact, but the striker's header from 10 yards was sent straight into Schmeichel's hands.
"Of course it was an emotional game", Poulsen told reporters. Cueva then took and missed, hitting it over the bar.
Play continued, but in a room somewhere in Moscow the Video Assistant Referees were checking the footage and less than a minute later, play was stopped with Gassama going over to the sideline screens to view the incident.More news: Cautious ECB slams Euro, boosts stocks - CMC Markets
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Peru were pacy in their counter attacks but lost their way around the box as one gilt-edged chance after another was wasted.
After being awarded a penalty via VAR, the 26-year-old skied his effort from the spot and was consoled by his team-mates as they walked off at the end of the half.
Peru are back at the World Cup after a 36-year absence and face Denmark for the second time ever.
"They got very little and probably deserved more - sometimes that happens".
Kasper Schmeichel - son of former Manchester United goalkeeping legend Peter - was showered with praise after his acrobatic display helped earn Denmark a 1-0 over Peru on Saturday to get their World Cup off to a flying start.
They also gathered around the city's main cathedral, playing music and bringing a touch of the South American party spirit.