Southampton advanced to the FA Cup fourth round after Adam Armstrong capitalized on a second-half error by Crystal Palace goalkeeper Vicente Guaita.
Armstrong charged down Guaita’s attempted clearance, leaving him with a simple finish.
Odsonne Edouard had given Palace the lead, but James Ward-Prowse leveled with a free-kick that was meant to be a cross.
Armstrong completed the turnaround at Selhurst Park in 22 minutes.
“I’m delighted with the overall performance,” said Southampton manager Nathan Jones, whose only previous win since replacing Ralph Hasenhuttl in November came against League One Lincoln City in the Carabao Cup.
“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, with only two changes from Wednesday’s 4-0 Premier League defeat at the hands of Tottenham.
In the early stages, the Eagles were far superior, with Zaha denied by Lyanco’s sliding challenge before having a fierce effort deflected wide by Duje Caleta-Car.
Palace’s talismanic winger then turned provider, releasing Edouard to open the scoring with a low finish past keeper Gazunu.
Southampton, who made five changes from the team that lost to Nottingham Forest for the sixth time in a row in midweek, lacked cohesion and were fortunate not to fall further behind when Jordan Ayew rattled the crossbar from Michael Olise’s low cross.