It is the second year in a row that Sekhukhune have made the last eight, having also been beaten finalists in 2023, and it took a superb strike to win the game.
Letlapa picked up the ball 35 yards from goal and arrowed a shot into the corner on 55 minutes for one of the goals of the campaign to date.
It was a deserved win for the Limpopo club, who largely dominated proceedings and ensured they would be the fifth top-flight side into the quarter-finals.
With defending champions Kaizer Chiefs, Orlando Pirates and Mamelodi Sundowns all already out of the competition, coach Eric Tinkler may feel this is their year.
Spears became just the fourth amateur side to reach the Nedbank Cup quarter-finals when they beat fellow ABC Motsepe League team CR Vasco da Gama 1-0 at the Mxolisi Dicky Jacobs Stadium.
Spears wrote their name into history thanks to Itumeleng Olyn’s 41st-minute winner, following in the footsteps of Baroka FC (2011), Summerfield Dynamos (2022) and Dondol Stars (2023) in making the last eight.
Baroka are the only third-tier team to have advanced to the semi-finals, when they famously defeated Kaizer Chiefs in the quarter-finals 15 years ago.
Spears have beaten two third-tier sides to make it this far, having dispatched FC Cardinals in the Last 32. Vasco’s cause was not helped by a red card after 53 minutes for captain Mogamat Bull.
Mkhambathi FC could not join them after they lost 3-0 to second-tier high-flyers Milford FC in a KwaZulu-Natal derby.
Mkhambathi held their opponents until midway through the second half, before Milford seized control of the contest.
Bulelani Sigomoshe gave them the lead on 67 minutes, netting for the second game running but his first in the Nedbank Cup.
Siphosethu Ndlabi added a second on 76 minutes, and when Tonny Mbunga scored his first goal in senior football on 88 minutes, the contest was over.
It is the first time Milford have won a Nedbank Cup game outright despite making the second round three years in a row, needing penalties and a bye in the past.
This will be their first visit to the quarter-finals, with that draw to take place on Monday at 19h00.
