Usuthu become the first name in the last-eight draw and were deserving of their victory as they created the better chances and controlled the game for the most part.
AmaZulu reach the quarter-finals for only the second time since 2012, as they look for a repeat of their 2010 final appearance, where they lost to BidVest Wits in the decider.
They were unfortunate not to receive a penalty in the first half when a trailing leg from Sbani Mntungwa caught Usuthu’s Nkosikhona Radebe in the box and, although the player went down, referee Thando Ndzandzeka waved play on.
It was a half of few chances at either end, but the visitors went in front 10 minutes into the second period.
Keagan Allen crossed from the right and the ball fell kindly on the edge of the six-yard box for Ekstein, and his chip over the keeper landed in the goal.
It was a fine, instinctive finish from the midfielder, who now has five Nedbank Cup goals to his name and a first since netting against Orlando Pirates in a losing effort in April 2024.
Richards Bay goalkeeper Ian Otieno made an excellent stop to deny AmaZulu a second, while at the other end Darren Johnson had to move smartly to deny Simphiwe Mcineka’s header.
Usuthu striker Thandolwenkosi Ngwenya had a clear sight of goal with no defender in sight but spurned the chance to end the contest when he completely miscued his shot.
But it is back-to-back away wins for AmaZulu in this year’s competition after they ousted Polokwane City in the Last 32.
The action continues on Saturday with four fixtures, including a visit for Mamelodi Sundowns to TS Galaxy (kick-off 15h00) and Orlando Pirates at home to second-tier Casric Stars (18h00).
Topflight Durban City are away to Motsepe Foundation Championship side Upington City (15h00), while Lamontville Golden Arrows host Stellenbosch FC at the King Zwelithini Stadium.