Alhassan Yusuf opened the scoring for Nigeria before Tolu Arokodare came off the bench to deliver a match-winning performance with two second-half goals.
The Super Eagles made a bright start and took the lead in the third minute. Akor Adams won possession and combined with Ademola Lookman, who set up Yusuf to finish from close range.
However, Tanzania responded strongly and drew level in the 32nd minute through Alphonce Msanga, punishing a defensive lapse by the Nigerian side.
Both teams went into the half-time break with the score at 1-1, leaving Nigeria with work to do after failing to capitalise on their early advantage.
Arokodare inspires second-half revival
Nigeria returned from the break with greater attacking urgency, and their improvement paid off in the 52nd minute.
Arokodare restored the hosts' advantage after a well-worked move involving Moses Usor and captain Wilfred Ndidi.
The striker then doubled his tally eight minutes later, controlling a dangerous delivery from Usor before producing a clinical finish to make it 3-1.
The two goals underlined the importance of Nigeria's attacking depth, with Arokodare making a decisive impact after entering the game as a substitute.
Super Eagles strengthen AFCON qualification hopes
The victory gives Nigeria three important points in Group L after their disappointing 3-0 defeat to Guinea-Bissau in September.
It also provides a confidence boost for Éric Chelle's men as they prepare for the return encounter against Tanzania in Zanzibar on Tuesday, 17 November.
Nigeria will now look to maintain their winning momentum and strengthen their position in the race for the 2027 AFCON, which will be hosted by Kenya, Tanzania and Uganda.