Ajibu, who had replaced Kenyan striker Paul Kiongera, pounced on a rebound to bang in after Ugandan striker, Hamisi Kiiza, was denied by the side post.
The win has helped Simba wrestle the third position from Mtibwa Sugar in the standing despite the two teams being level on points.
Both teams have collected 27 points from 13 outings but Simba have a better goal difference.
Simba and Ndanda attacked in turns in the first half but neither managed to find the back of the net, finding them stale at the breather.
Ndanda striker Atupele Green failed to convert with a clear opportunity early in the first half, when he was set up inside the box but shot wide.
Simba coach Dylan Kerr’s decision to introduce midfielder Said Ndemla for Ugandan Brian Majwega on the 65th minute paid off as the team eventually managed to make occasional forays into the Ndanda penalty area.
Kerr also rested midfielde, Mwinyi Kazimoto for Awadh Juma on the 89th minute.
Ndanda coach Hamimu Mawazo also opted for substitution on 65 minutes, in which he brought in Mohamed Ally for Aziz Sibo but the substitution did little to help the team change the course of the game.
The win over Ndanda has helped the Msimbazi Street side to end a string of less impressive results in recent games.
Simba were forced to a 1-1 draw with Toto Africans of Mwanza at the CCM Kirumba in Mwanza on December 19.
The side then managed another 1-1 result in a game against Mwadui FC of Shinyanga at the Kambarage Stadium on December 26.
Simba skipper, Kazimoto, admitted that the game was tough and insisted that although his team managed a slim win, grabbing three points mattered the most.
Ndanda skipper Kigi Makasi said his team played well but committed minor mistakes that eventually cost the squad.