Yohan Cabaye's 38th minute strike proved to be the difference between the two teams as the home side extended their unbeaten run in the Premier League to three games.
Saints have now lost three of their past for league matches and slipped to 12th on the Premier League ladder.
Cabaye is proving to be worth every cent of the club-record £10million fee Palace paid for the French international. The 29-year-old is a difference maker, who has the ability to single-handedly change the course of a match with his individual talent.
Southampton were left ruing their inability to turn 56% of possession and 15 shots at goal into clear-cut goal-scoring opportunities as their barren run of form in recent weeks continued.
Another home win makes this Sunday even happier! #eaglespic.twitter.com/JE0SzLbCKV
— Connor Wickham (@ConnorWickham10) December 13, 2015
Great win, fantastic atmosphere, well done lads. #cpfcpic.twitter.com/DqbDUfjQql
— yohan cabaye (@YCabayeofficiel) December 12, 2015
Great 3 points on to the next #cpfc#team243 Godisgreat pic.twitter.com/BzxjCNeD43
— Yannick Bolasie (@YannickBolasie) December 12, 2015
"It was a tough game - Southampton really applied themselves well but I thought we edged it in certain areas. Our wide players were terrific, but the difference between the two sides was a masterclass in midfield from Cabaye. He showed every reason why we spent the pennies to bring him here."
"I'm disappointed about the final result, but not in the performance of the team. The wind made it very difficult to play our football. Maybe it suited Palace more because they play more direct than we do, but we controlled it for 20 minutes but then they scored. We were the better team in second half and dominated, and we're disappointed not score in the last seconds.