Guinea took a first-half lead with a superbly-taken goal by Sory Kaba in the 34th minute of the Group B game.
But the Malagasy stunned their opponents with goals from Anicet Abel and Carolus Andriamatsinoro early in the second half before Francois Kamano spared Guinea's blushed by equalising with a penalty in the 66th minute.
Early in the day, Uganda stunned Democratic Republic of Congo with a 2-0 win in Group A while Nigeria needed a late goal to beat Burundi, another team making their debut at the tournament.
Nigeria top the group with three points, followed by Guinea and Madagascar on one and Burundi on none.
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Guinea midfielder Naby Keita, who suffered an abductor injury with Liverpool in May, started on the bench but was brought on in the second half.
"If Mohamed Salah doesn't play for Egypt or Sadio Mane doesn't play for Senegal, that makes a difference, you have to be realistic," said Guinea coach Paul Put, adding that Keita decided he could not start.
"It's not my fault, it's Naby's decision and we have to respect his decision."
Guinea dominated the first half and broke the deadlock in the 34th minute. Amadou Diawara lofted a through ball over the Malagasy defence into the path of Kaba, who lobbed the ball over goalkeeper Melvin Adrien, spun around and slipped the ball into the empty net.
But the West Africans were stunned by two quick goals early in the second half.
Abel rose at the near post to head in a corner in the 49th minute before Andriamatsinoro ran on to a long ball and fired past Aly Keita to put the underdogs ahead six minutes later.
That prompted Guinea to bring on Keita and they almost immediately equalised.
Ibrahima Traore charged into the area and went to ground, the referee judged that he had been fouled and Francois Kamano calmly converted the penalty.
(Reporting by Brian Homewood; editing by Tony Lawrence and Ed Osmond)
