The Citizens extend their unbeaten run in the league to six matches. Chiefs were unlucky to lose, having had the better of the chances only to be denied by a string of top-notch saves from Cape Town City goalkeeper and man-of-the-match Peter Leeuwenburgh.
In contrast to his opposite number, Chiefs goalkeeper Virgil Vries was the pantomime villain as he let a rudimentary free-kick slip through his hands for Edmilson Dove to poke home.
The away side were dealt an early blow when their top goalscorer Siphelele Mthembu was stretchered off with an ankle injury after a heavy tackle by Teenage Hadebe and replaced by the experienced Kermit Erasmus.
Amakhosi then had a gilt-edged opportunity in the sixth minute when Khama Billiat's free-kick was headed just wide of Leeuwenburgh's post by Daniel Cardoso.
The Soweto Giants were playing some high tempo, fluid football and came close again in the 18th minute when Bernard Parker found Billiat with a well-executed backheel in to the path of the Zimbabwean marksman whose shot was well palmed away by Leeuwenburgh.
Chances were coming thick and fast for both sides as soon after, the Citizens almost scored completely against the run of play after brilliant work down the left-hand side by Gift Links who fed in Thabo Nodada but the striker's effort was parried away by Virgil Vries.
In the 30th minute, Billiat was put through on goal by Hendrik Ekstein, but Leeuwenburgh saved well - this time with his feet. It was a mystery as to how the score was still 0-0 with the number of chances created by both sides as the sides headed in to the interval.
Both sides made changes at half-time with eventual goalscorer Dove coming on in place of Teko Modise and Leonardo Castro replacing Bernard Parker.
In contrast to the first half, chances were few and far between in the opening quarter of an hour. Perhaps both sides had been given some harsh words by their respective managers about tightening up defensively.
The away side were much-improved in the second half and began to control proceedings in midfield. The best chance of the second half, however, fell to Chiefs. After sloppy play by City in giving the ball away in midfield, Billiat put Castro in to some space down the left-hand side, with the Uruguayan letting fly from just inside the box only for Leeuwenburgh to pull off another top-notch save.
Soon after, Siphelele Ntshangase hit the woodwork after his shot took a wicked deflection of Kwanda Mngonyama with Leeuwenburgh completely beaten.
Virgil Vries made another howler bringing back memories of his shocker in the Sundowns game when he spilled a rudimentary free-kick delivery from Links. Replacement left-back Dove was the quickest to react to poke the ball in to an empty net and stun the Amakhosi faithful.
The Citizens were then reduced to ten men when Zukile Kewuti was given a straight red card for his reckless challenge on Ntshangase, giving the home side an opportunity to get back in to the game
But Chiefs were unable to capitalise on their numerical advantage as the visitors held on for a massive win.
Chiefs: Vries, Ntiya-Ntiya, Cardoso, Hadebe, Moleko, Katsande, Ekstein, Mashiane, Ntshangase, Parker, Billiat.
Subs: Bvuma, Gordinho, Ngezana, Moon, Mahlasela, Zuma, Castro.
City: Leeuwenburgh, Mkhize, Cupido, Kewuti, Mngonyama, Nodada, Martin, Modise, Mokeke, Mthembu, Links
Subs: Stephens, Seedat, Norodien, Dove, Patosi, Ralani, Erasmus.