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...
