Midfielder Pius Buswita and striker Amissi Tambwe notched the goals to steer their team to the next stage of the tournament.
Yanga had to step up their game to come out with the win given they faced stiff opposition from their opponents, who participate in the National Second Division League.
Reha goalkeeper, Idrissa Ramadhan, stood firm between the posts on the fifth minute to foil an effort by Yanga defender, Nadir Haroub, who had attempted to head in a corner kick.
Midfielder Pius Buswita got the better of Reha defender close to the latter's penalty area, whipped in a cross, only to see the chance go begging.
Ramadhan made a good save to keep Yanga's left fullback, Gadiel Michael, at bay on the 14th minute after the latter had been set clear inside the former's area.
Buswita had an opportunity to notch the opener for Yanga on the 16th minute, in which he collected the ball within Reha's box, only to attempt a right footer which flew way over.
Reha's best opportunity during the early exchanges came on the 22nd minute after the outfit's striker, Idriss Omary, was set clear inside Yanga's penalty area and saw his left foot effort go off the left post.
Yanga failed to make the most of two free kicks a few meters from their opponents' penalty area thereafter.
Yanga striker, Yusuf Mhilu, arrived late inside Reha's box and missed a good cross by winger, Emmanuel Martin, from the left two minutes from the breather.
Striker Rajab Sentumbi, arrived late inside Yanga's box and missed a cross by team mate on the 52nd minute, throwing overboard a glorious opportunity to put Reha FC ahead.
Mhilu attempted a right foot shot within Reha FC's 18 yard area several minutes later and the latter's goalie, Ramadhan, saved the effort.
Yanga went close on the 70th minute in which Reha keeper Ramadhan saved a header by Yanga midfielder, Pappy Tshishimbi, within the 18 yards.
The agile Reha keeper made a good save two minutes later, palming away a fierce left foot shot by Yanga defender, Gadiel Michael, from 20 meters out.
Rajab Audasi failed to make the most of Yanga's failure to clear a cross on the 77th minute, as his right foot shot from inside the area went off target.
Buswita notched the opener for Yanga on the 82nd minute, beating Reha keeper, Ramadhan, with a right foot screamer from outside the area.
Tambwe, who has yet to play for Yanga in the Mainland Premier League as he had been sidelined by an injury, put Yanga 2-0 up on the 85th minute, heading in a lob by team mate.
The victory helped Yanga avoid the fate that rivals, Simba SC, experienced in the tournament, as the latter were bundled out by the Second Division League's outfit, Dar es Salaam's Green Warriors,
Dodoma FC progressed to the next stage of the event after recording a 1-0 win over Coastal Union at the Mkwakwani Stadium in Tanga the same day.
Reliants Lusajo drilled in for Dodoma FC on the 19th minute, released outside the area, beat Coastal Union's goalie, Hussein Shariff, with a left foot shot.
Dodoma FC lined up players with plenty of experience in domestic soccer, namely Lusajo, Shija Mkina, Mussa Hassan, Nassor Masoud and keeper Jackson Chove.
Dodoma FC opted for a defensive approach after the breather and managed to hold on for the win.