The flashes of brilliance by the inform pair lit up this initially dreary encounter at KaNyamazane Stadium in Mpumalanga.
The Strasbourg player, Nkambule opened the scoring in the 81st minute. Receiving a loose ball outside the penalty area, the diminutive playmaker swept past a cluster of Botswana defenders before firing a low shot past the badly exposed Basimanebothle Moilwa in goals for the visitors.
Man of the Match, Manyisa put the result beyond doubt three minutes from the end when he curled in a thunderbolt from outside the 18-yard box past a hapless Moilwa to send the appreciative crowd into frenzy.
The top of the table affair failed to live up to expectations in the first half as the teams sweated it out under searing temperatures and gave a scrappy show.
In the few occasions that the hosts created scoring opportunities, the frontline fired blanks with Manyisa and Wayne Matle the chief culprits, while Nkambule had a ferocious shot smothered by Moilwa.
Bongani Twala could have opened the scoring earlier in the 21st minute but headed over from six yards.
The second half saw a revitalized Amajita knit precise passes and in one such occasion, in the 47 the minute, Sibusiso Ntuli forced a brilliant save from the Botswana goal minder.
Ntuli was back among the misfiring culprits with the miss of the day when he shot wide with Moilwa at his mercy in the 80th minute.
Relentless Amajita were rewarded after a flash of brilliance by Strasbourg’s Nkambule when he breached the resolute Young Zebras defence.
Manyisa put the result beyond doubt in the 85th minute with a long-range effort.
The visitors’ woes were further compounded in the 90th minute when Gabriel Bokutlho was sent off after a second bookable offence.
Amajita will meet Madagascar in the semifinals on Friday after the Islanders progressed with a 2-0 over Swaziland.