Balkissa Sawadogo scored the decisive goal 10 minutes from time as Burkina Faso made their numerical advantage count after Tanzania were reduced to 10 players early in the second half.
Tanzania made the brighter start and almost took the lead within moments of kick-off when captain Opah Clement Tukumbuke raced through on goal, but she fired her effort over the crossbar. Donisia Minja also went close with a long-range free-kick that drifted just over the target.
Burkina Faso gradually settled into the match and created chances of their own. Adama Congo missed from close range before Tanzania thought they had opened the scoring through Tukumbuke. However, a VAR review ruled out the goal for a foul and accidental handball, with the striker also shown a yellow card.
Burkina Faso made the breakthrough just before half-time. Adele Kabre reacted quickest after a defensive mistake and calmly lifted the ball over goalkeeper Najat Idrisa to give her side a 1-0 lead.
The West Africans almost doubled their advantage in first-half stoppage time, but Idrisa produced an excellent save to deny Balkissa Sawadogo.
The match turned in Burkina Faso's favour 10 minutes into the second half when Tanzania's Hasnath Ubamba was sent off following a VAR review for a dangerous challenge on goalkeeper Nina Dabilgou.
Despite being down to 10 players, Tanzania responded brilliantly. Minja's powerful free-kick was tipped onto the crossbar by Dabilgou, but Aisha Mnunka reacted quickest to the rebound to score the equaliser in the 62nd minute.
Burkina Faso continued to push for a winner, while Tanzania nearly gifted them another goal after a defensive mix-up saw Julitha Singano's effort flash just wide of the post.
The pressure finally paid off in the 80th minute. After Juliette Nana's shot was blocked, the ball fell kindly for Balkissa Sawadogo, who found space between the Tanzania defenders and calmly finished past Idrisa to restore Burkina Faso's lead.
Tanzania pushed forward in the closing stages in search of another equaliser, but Burkina Faso defended well and survived one final scare when a last-minute attack was cleared away.
The victory gives Burkina Faso their first three points of the tournament, while Tanzania were left to rue missed chances and the costly second-half red card.
