Tanzania coach Marcio Maximo was sent off during Saturday's game
Senegal failed to go clear at the top of Group Seven when they were held 0-0 in Mozambique on Sunday in the 2008 African Cup of Nations qualifiers.
The Teranga Lions are now only ahead of Tanzania at the top of the group thanks to their better head-to-head record between the two sides.
Tanzania moved onto eight points on Saturday thanks to their 1-0 win in Burkina Faso.
The encounter in Ouagadougou on Saturday saw the hosts comfortably in charge but failing to capitalise on their opportunities.
Burkinabe frustration boiled over in the second half when defender Moussa Ouatara was sent off after head butting Amir Maftah.
The visitors also had their fair share of trouble as Shadrack Nsajigwa and coach Marcio Maximo were also dismissed as tempers flared.
The Taifa Stars punished the home side for being profligate midway through the second half.
Henry Joseph beat the offside trap and chipped the ball over the keeper to give Tanzania a crucial win that sees their hopes of qualification given a major boost.
Burkina Faso remain bottom of the table on four points while Mozambique are just two points ahead of them.