A second-half brace from Tolu Arokodare and an early strike from Alhassan Yusuf helped the Super Eagles return to winning ways after their disappointing 3-0 defeat to Guinea-Bissau in their previous Group L encounter.
Eric Chelle's men made a flying start, taking the lead in the second minute through Yusuf, who calmly finished after receiving a pass from Atletico Madrid star Ademola Lookman.
However, the Taifa Stars fought back and drew level in the 33rd minute when Alphonce Msanga converted a pass from Novatus Miroshi to beat goalkeeper Stanley Nwabali.
Three-time African champions Nigeria suffered another setback shortly before half-time when Lookman picked up an injury and was replaced by Moses Simon.
With the score at 1-1 at the break, Chelle made two changes, bringing on Arokodare and Moses Usor in place of Tochukwu Nnadi and Yusuf.
The substitutions paid off almost immediately as the Ajax star restored Nigeria's lead with a finish in the 52nd minute, finishing a move involving captain Wilfred Ndidi.
Arokodare struck again eight minutes later after controlling a cross from Usor before drilling home with his left foot to complete his brace.
The Ajax striker now has eight goals in his last six games for club and country.
Tanzania struggled to find a response as Chelle’s men controlled the closing stages to secure their second victory of the qualifying campaign.
The result takes the three-time African champions to six points from three matches, leaving them second in Group L, one point behind leaders Guinea-Bissau, who drew 1-1 with Madagascar on Thursday.
Nigeria will now turn their attention to Tuesday's return fixture against Tanzania in Zanzibar as they look to strengthen their chances of reaching the continental tournament.
The West Africans secured third place at the 2025 Africa Cup of Nations in Morocco after defeating Mohamed Salah’s Egypt on penalties at the Mohammed V Stadium in Casablanca.
