Crystal Palace goalkeeper Vicente Guaita made a second-half error that allowed Adam Armstrong to score the winning goal.
Guaita's attempt at a clearance was charged down by the other.
Palace had taken the lead, but James Ward-Prowse hit a free-kick that was supposed to be a cross to equalize.
The turn around took 22 minutes from time to time.
Nathan Jones' only previous win was against League One Lincoln City in the Carabao Cup.
The response has been great after a tough week.
We showed the side we can be after we began to be a bit cautious. At half-time, we made a few changes and came out aggressive.
Edouard and Will Hughes were restored to the side in the only changes from the loss to Spurs.
The Eagles were the more accomplished outfit in the early stages, with Zaha denied by Lyanco's sliding challenge before having a fierce effort diverted wide by Duje Caleta- Car.
The talismanic winger turned provider moments later, releasing Edouard to open the scoring with a low finish.
The Saints, who made five changes to the team that suffered a sixth successive league defeat against Forest on Wednesday, lacked cohesiveness and were fortunate not to fall further behind when Jordan Ayew hit the woodwork.
When Ward-Prowse's delivery evaded everyone and snuck inside the far post, there were audible boos from the travelling supporters.
In the beginning of the second period, there were few clear-cut opportunities. Zaha sent a first-time shot off target from another Olise delivery.
When Guaita got a strong hand to the ball, it looked like it was drifting towards the far corner, but moments later he made a mistake that led to the winner.
Despite a late push by Palace, Saints held on for a win that could give them a much needed boost.
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