Galaxy were comfortable 2-0 winners over third-tier Jacksa Spears, while Durban City needed penalties to defeat local rivals Lamontville Golden Arrows after the sides played to a 1-1 draw. The shoot-out ended 5-4.
They join second-tier sides Casric Stars and Milford FC in the semi-finals after the latter two advanced past topflight Sekhukhune United and AmaZulu FC on Saturday.
The semi-final draw will take place on Monday evening on SuperSport Channel 202 from 20h30.
Galaxy earned their first Nedbank Cup semi-final since they lifted the trophy in 2019 when they eased past Spears, who gave a good account of themselves at the Solomon Mahlangu Stadium.
The Rockets took the lead on 34 minutes when Brazilian Igor Silva headed into the net from Patrick Fisher’s cross for his first goal in South African football since he arrived at the start of the season.
Tshepo Kakora made the tie safe when he added a second just before the hour mark, which was also his first goal for the club following his move from Magesi FC.
Spears had their opportunities and struck the crossbar in the second half, but their club-record campaign came to an end with the defeat.
Galaxy have yet to concede in the Nedbank Cup this season after seeing off Marumo Gallants, Mamelodi Sundowns and now Spears, all home ties.
Five of their last six Nedbank Cup matches have been played at home and they will hope for the same again in Monday’s draw.
Durban City took the lead at the King Zwelithini Stadium on 36 minutes as Fezile Gcaba blasted the ball into the back of the net from close range after being set up by Saziso Magawana.
That was the way it stayed until just before the hour mark when Golden Arrows equalised through Thokozani Khumalo as he headed in Ayabulela Maxwele’s cross from the right.
City were reduced to 10 players when Athini Jodwana deliberately handled the ball and received a second yellow card, and Khumalo then posted a contender for miss of the season when he fired wide of an empty net from eight yards.
The match went to penalties and for Golden Arrows it was a sense of déjà vu. They have now been involved in five shoot-outs in the Nedbank Cup since 2008 and lost all of them.
City made it a hat-trick of wins via spot-kicks in this year’s competition as they reached the semi-finals without winning a game outright.
When you include their quarter-final loss on penalties to Marumo Gallants last season, it means their last four Nedbank Cup fixtures have been decided via spot-kicks.