Goals from Inter Milan forward Keita Balde and a second half stunner from Keprin Diatta handed Aliou Cisse’s men the three points against Emmanuel Amuneke's side.
Aishi Manula started in goal for the Taifa Stars, with Kelvin Yondani and Gadiel Michael leading the defence while captain Mbwana Samatta spearheaded the attack.
Aliou Cisse started Keita Balde, Ismaila Sarr and Mbaye Niang in attack and could have been rewarded after a fine combination in the seventh minute.
Badou Ndiaye beat his marker and played Niang through on goal, but the Rennes forward missed the target from close range.
Relief came to Senegal, who dominated the first half, when Idrissa Gueye set up Balde in the 28th minute and he fired past goalkeeper Aishi Manula for the opener.
Senegal had a chance to double their lead through Niang but the forward missed the chance and just before the half-time break, another opportunity fell to Gueye, but he too failed to hit the target.
The second half continued in a similar fashion with Senegal dominating the early proceedings and could have doubled their lead through Keprin Diatta, but his header was saved by Manula.
Tanzania seemed to regain their confidence in the second half and gradually grew into the game but failed to seriously threaten Senegal’s defence.
Diatta made amends for his earlier miss when he fired in a stunning strike from 18 yards to seal the victory for the West Africans, and was duly named the Man of the match.