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.”
Tshepang Moremi scored a stunning long-range goal as Orlando Pirates advanced to the semi-finals of the Carling Knockout Cup after a 2-1 victory against Magesi at the Orlando Stadium.
Durban City coach Gavin Hunt has expressed his disappointment after losing to Richards Bay in extra-time during Sunday's Carling Knockout quarter-final.
TS Galaxy coach Adnan Beganovic admits it was always going to be difficult for his side to progress in the Carling Knockout, following their 2-1 quarter-final, extra-time defeat to Golden Arrows.
Golden Arrows defeated TS Galaxy 2-1 after extra time in their Carling Knockout Cup quarter-final encounter at the King Goodwill Zwelithini Stadium on Sunday.
