Adam Armstrong capitalised on a second-half error by Crystal Palace goalkeeper Vicente Guaita to earn Southampton a place in the FA Cup fourth round.
Guaita’s attempted clearance was charged down by Armstrong, who was left with a simple finish.
Odsonne Edouard had put Palace ahead, but James Ward-Prowse equalised with a free-kick that was intended as a cross.
Armstrong completed the turnaround 22 minutes from time at Selhurst Park.
Southampton manager Nathan Jones, whose only previous win since replacing Ralph Hasenhuttl in November came against League One Lincoln City in the Carabao Cup, said: “I’m delighted with the overall performance.
“It’s been a tough week, but the response has been fantastic.
“We started a bit edgy, but we showed real zest after that and showed the side we can be. We tweaked a few things at half-time and came out aggressively.”
Palace manager Patrick Vieira fielded a strong team, restoring Edouard and Will Hughes to the side in the only changes from Wednesday’s 4-0 Premier League defeat by Tottenham.
The Eagles were by far the more accomplished outfit in the early stages, with Zaha denied by Lyanco’s sliding challenge before having a fierce effort deflected wide by Duje Caleta-Car.
Palace’s talismanic winger turned provider moments later, releasing Edouard to open the scoring with a low finish beyond keeper Gavin Bazunu.
Southampton, who made five changes to the team that suffered a sixth successive league defeat against Nottingham Forest in midweek, lacked cohesion and were fortunate not to fall further behind when Jordan Ayew rattled the crossbar from Michael Olise’s low cross.
There were audible boos from the travelling supporters midway through the first half as Southampton struggled to breach the Palace defence, but they restored parity out of nothing when Ward-Prowse’s inswinging delivery evaded everyone and snuck inside the far post.
Clear-cut opportunities were few and far between in a more even start to the second period. Zaha sent a first-time shot off-target from another Olise delivery, but Southampton grew in confidence the longer they kept Palace at bay.
Armstrong’s looping header from Ainsley Maitland-Niles’ cross appeared to be drifting towards the far corner until Guaita got a strong hand to the ball, but moments later he made the mistake that led to Armstrong’s winner.
Palace – semi-finalists last season – rarely looked like fashioning an equaliser despite a late push as Southampton held on for a win that could give their faltering campaign a much-needed boost.
