The West Ham attacker scored a late stunner to earn the three points after Bogdan Stancu's second-half penalty had cancelled out Giroud's opener.
Javier Hernandez and Oribe Peralta both scored as El Tri advanced to the last eight at the centenary tournament, while sending Uruguay home.
Dunga had hoped that the large number of Brazilians in Florida would turn up at and get behind the Selecao, and although he was mistaken his team took care of business.
The Arsenal striker continued his recent good form at international level with Arsenal team-mate Laurent Koscielny also on target in a comfortable victory over the Scots.
The Selecao will take to the field against Ecuador on Saturday without a single one of those who participated in the infamous World Cup semi-final defeat to Germany two years ago.
The Portugal superstar scored the decisive spot-kick as Los Blancos claimed their 11th European Cup with a 5-3 penalty shoot-out victory over Atletico Madrid after extra time.
The Sweden international netted a superb double to sign off from PSG in style, and was joined on the scoresheet by midfielder Blaise Matuidi and fellow attacker Edinson Cavani.
The former Gunners defender believes the Chilean has the work ethic and charisma to compare to the stars of the famous 2003-04 unbeaten title-winning side.
The Poland international showed just how finely tuned his technique is on the training pitch with immense but casual control over the ball in just a pair of socks.
The five-time Ballon d'Or winner has admitted everybody at the Catalan club wants Zinedine Zidane's men to finish the 2015-16 campaign trophyless, while his side win the domestic.
Laurent Blanc's men made more history in Corsica on Saturday, with the Uruguay international striker very much the star of the show in a routine success.