Simba grabbed the first goal on the first minute through Jamal Mwambeleko, who beat Mwenge keeper Mudathir Hamisi with a header off a cross from tyhe left side.
Striker Hamad Ali brought Mwenge to level terms on the 29th minute, beating Simba's keeper, Emmanuel Mseja, with a right foot shot from inside the area, following failure by a Simba defender to foil the former;'s move.
The visitors could have added the 38th minute, after striker, Moses Kitandu, had been released by midfielder Said Ndemla inside Mwenge's area and unleashed a left foot shot which, though, hit the crossbar.
Simba's technical panel decided to ring changes in their team early in the second stanza, bringing in wingers Shiza Kichuya and Ghanaian Nicholas Gyan, and forward John Bocco in place of Mwambeleko, Juma Luizio and Kitandu.
Gyan immediately got into action, shooting over from within Mwenge's 18 yards on the 48th minute after he was released by Kichuya
The Ghanaian again easily missed a sitter six minutes later, as he frustratingly shot over from within Mwenge's 18 yards after he was set up by Kichuya.
Bocco failed to convert a good opportunity a few minutes later, blasting over from within the area as he attempted to slot home a low cross by left fullback Mohamed Hussein.
Mwenge defender came to his team's rescue on the 80th minute as he made a goal line clearance to keep Bocco at bay.
The day also saw Singida United cruise to a 3-2 win over Zimamoto at the same venue.
Winger Deus Kaseke scored the opener for Singida United on the seventh minute, easily beating Zimamoto keeper inside the latter's area after thje former had been released by forward, Kambale Salita.
Danny Usengimana put the visitors 2-0 up on the 21st minute, as he connected home a pinpointcross by right fullback, Miraji Adam.
Zimamoto managed to reduce the margin in the latter stages of the first stanza through dependabl;e goal getter Ibrahim Ahmada who lobbed the ball over Singida United keeper, Ally Mustafa, after the former had been put lear outside the area.
The visitors' midfielder, Kigi Makasi, drilled in the third, on the 81st minute, as he beat Zimamoto keeper with a left foot shot from inside the latter's area.
Ahmada quickly slotted in the second for Zimamoto on the 84th minute, as he again lobbed the ball over Mustafa from outside the area.