Bokang Mokwena gave City the lead in the 54th minute at the Richards Bay Stadium but Knox Mutizwa levelled with 84 minutes played to take the tie to extra-time.
Substitute Mbulelo Nombengula then fired home to put the hosts ahead and Lundi Mahala added a third goal with 120 minutes on the clock to seal Richards Bay's progression to the semi-finals.
Speaking after the game, a delighted Gabriel said on IOL: "I think the writing was on the wall because today it was all us here except for the first 10 minutes of both halves in regulation time. We were good today, the display was fantastic.
"The opposition failed to keep up with the pace of the game, we played the game at a really high tempo, and the quickness of our players made it hard for the opposition."
Gabriel added: "Winning this cup would be huge for the club and everyone associated with it. We want to try and win it, we will give it our all.
“We believe that there's an opportunity to grab it, and hopefully luck runs our way, a few moments go our way, and you know how football goes; you can end up with a cup in the blink of an eye.”
Golden Arrows became the first team to book their place in the Carling Knockout quarter-finals after thrashing Chippa United 4-0 at King Zwelithini Stadium on Saturday afternoon.
AmaZulu and Sekhukhune United are among the favourites to progress ahead of the upcoming four Carling Knockout Cup Round of 16 fixtures this weekend.
Polokwane City captain Bulelani Nikani is hopeful that victory against Siwelele in their Carling Knockout Cup last 16 match on Saturday will kick-start their season.
Dimitar Pantev is hoping for a fast start to his Richards Bay tenure after his recent appointment as a replacement for sacked former head coach Ronnie Gabriel.
