Maritzburg captain Kurt Lentjies decided the encounter with a sweetly struck free-kick in the 84th minute at Harry Gwala Stadium to give his side a third straight victory and bolster their top-eight ambitions.
It was far from a pretty match, but other positives from the display include young midfielder Mlondi Dlamini's fearless showing down the right channel, while rising talent Lebogang Maboe's game is getting better ever time he enters the field.
"First of all this win secures us from relegation mathematically and this three points take us out of that equation," Davids told reporters after his side bolstered their tally to 35 points from 26 matches.
"Last season this time we were rooted at the bottom. So I'm really delighted for the players, the hard work they put in really paid off today.
"I think the performance was good and yes it was not pleasing on the eye because Cape Town City didn't play their normal game. That was due to us and the players following the tactical instructions. I don't think they really had one corner kick.
"To stop a team like Cape Town City in the way we did today was absolutely fantastic. The players will have to take all the credit to be able to follow everything what we were asking for."
The Team of Choice, in seventh spot on the table, only previously finished in the top eight under Steve Komphela in 2014/15 before his defection to Kaizer Chiefs.
Davids, however, is mindful his charges still have to face champions Mamelodi Sundowns and log leaders Bidvest Wits.
"Normally 42, 43 points secures you and we got to 35 now so it is still a long way to go in terms of the games," he added.
"We still have to collect points and you guys have said we still have to play Bidvest Wits and Mamelodi Sundowns. We are playing Platinum Stars and Bloemfontein Celtic at home. It it going to be a tough four games to be able to secure the top eight."
Maritzburg next visit Wits at Bidvest Stadium on Sunday.