Tunisia seemingly had the height advantage in Saturday's last-eight tie in Libreville with striker Taha Yassine Khenissi a particular nuisance.
But Burkina Faso refused to be bullied and Duarte's inspired decision to bring on Aristide Bance proved decisive as he opened the scoring with a fine drilled effort in the 80th minute, before Prejuce Nakoulma - whose pace had caused problems all game - rounded off a 2-0 win.
"First of all I'd like to pay tribute to my colleague [Tunisia boss Henryk Kasperczak], credit to him for the job he has done with Tunisia," Duarte told a post-match news conference.
"It was a difficult match, decided on the small details.
"We were afraid of that aspect [Tunisia's physicality], especially at corners and free-kicks because we knew they had athletic and tall players.
"In my team I don't have players that are tall, but I'm very happy with that victory because we are through to the semi-finals and can dedicate the win to the people of Burkina Faso. Both teams were very impressive, it wasn't easy.
"I knew Tunisia was [a] solid [team], very strong defenders, but I knew playing one to one we could take advantage of them."
Kasperczak was also in charge of Tunisia when they were beaten by Burkina Faso at the same stage in the 1998 AFCON.
And the Pole acknowledged that his team did not show the required energy to make the semi-finals.
"It's true we didn't have the same performance as in the past," he said. "We did not show fighting spirit or a willingness to win.
"We were tired, did not show the possession of ball as we have proved in the past and were not successful in transition.
"We tried to do better, but unfortunately the substitution made by my colleague proved positive, when a player makes a difference it shows the coach foresaw a change in the match, so congrats to the coach."
Kasperczak also played down an incident in which Wahbi Khazri seemingly snubbed his handshake when the forward was substituted just after the hour.
He added: "Whenever a player comes off he will not be happy, so it's normal."