The United winger struggled to make an impact in Portugal’s 1-0 defeat to Germany, but was mesmeric against the Danes, outshining Cristiano Ronaldo on the opposite flank.
The 25-year-old set up Portugal’s second goal for Helder Postiga, but Denmark responded with two Nicklas Bendtner strikes, before Silvestre Varela snatched victory for the Seleccao in the 87th minute.
"We showed everyone we wanted to win the game," Nani told reporters after the game. "When Denmark equalised, we had a lot of anger in us and a desire to turn things around.
"The only thing we were thinking about was the victory and we had to fight for it until the last minute. That is what I tried to transmit to my team-mates.
"Those last minutes were decisive. We had to give everything, to risk everything."
Ronaldo spurned several chances but Nani backed his ex-United colleague, saying: "Everyone misses chances. Cristiano is very important to us because he helps in defence and attack."
Portugal are third in Group B, level with Denmark and behind leaders Germany, who have won their first two games. Nani’s side face pointless Netherlands on Sunday.