The Taifa Stars need a win over Uganda in Dar-es-Salaam and will pray that Lesotho falters in Cape Verde.
Coached by Emmanuel Amunike, Tanzania will fancy their chances against an already-qualified Uganda.
Uganda are guaranteed to finish as Group L leaders, and forward Farouk Miya has stressed the need to finish this qualification campaign on a high.
“We are ready for the task ahead of us on Sunday and I know Tanzania will come with full force wanting to win the match to secure qualification but we also want to finish on a high. We shall give it our best shot,” Miya was quoted as saying by the Uganda football Federation website.
In the other Group L encounter in Praia, Lesotho are also vying for a maiden Afcon appearance with an away win over Cape Verde.
While winning away appears to be an insurmountable task for Lesotho, three points will be enough to see them make history without minding how Tanzania and Uganda play.
Elsewhere, Togo will be in Benin seeking nothing but victory to secure Afcon qualification from Group D.
Togo are in an unfamiliar fourth place in this group and only victory will take them to Egypt 2019.
Togo captain Emmanuel Adebayor has hinted at retiring after this match.
"It's quite possible that Sunday's match will be my last with Togo, whether we qualify or not,” Adebayor was quoted as saying by Radio France International.
“I would give the best of myself and after the match, we'll see. Now it's true that flying, coming to Lome, playing for the national team, it's not like before, it's not like in 2000 or 2001. I'm not 17 anymore, I'm 35 now and it's getting more and more complicated. But the nation needs me, I am obliged to answer the national team call,” he added.
Meanwhile, in Group G Zimbabwe are looking to book their Afcon ticket against Congo Brazzaville in Harare.
Just a point will see Zimbabwe qualify and Warriors vice-captain Ovidy Karuru is aware of the expectations on them.
“This is the match they were obviously looking forward to win given what is at stake. We cannot afford to lose the match and fail to qualify for the Afcon finals,” Karuru told The Herald.
While a draw will be enough for group G leaders Zimbabwe, Congo need to win this match to confirm their place at the Afcon tournament.
Lastly, the other Group G tie will see DR Congo welcome Liberia and a win for Florent Ibenge’s men should secure themselves qualification.