Charlie Austin put the home side ahead with a penalty after Shane Long was fouled by Martin Kelly's challenge.
Saints deservedly doubled their lead through midfielder Jake Hesketh's first goal for the club just after the hour.
Connor Wickham had Palace's best chance but failed to latch on to a loose back header from Jose Fonte inside the box.
Austin's fourth goal in the space of six days and three games gave Claude Puel's Southampton a deserved lead after half an hour.
Palace lost captain Scott Dann early on to a suspected hamstring injury and it was his replacement Kelly who was at fault in the build-up to the opening goal.
The central defender failed to control the ball with his chest and as it ran away from him Long gave chase and was tripped inside the box.
Long almost netted a goal of his own in the closing stages of the first half when he rounded Palace goalkeeper Wayne Hennessey, but his finish lacked power and allowed Damien Delaney to clear off the line.
Saints' continued pressure in the second half finally told as they doubled their lead through 20-year-old Hesketh.
Long drove into the box and when his shot was saved by Hennessey the rebound broke to Hesketh, who calmly swept a left-footed finish into the bottom corner.
Southampton midfielder Jake Hesketh told BBC Radio Solent:
"First and foremost we're through in the cup, but to score a (first senior) goal was perfect for me.
"It's a bit of a whirlwind really. It's come back to me nicely and then I've just run off.
"In my head I'm thinking, 'what am I doing here?' as I wasn't sure whether or not to celebrate with a knee-slide. But, it was brilliant.
"It's really nice and you feel really appreciated by the fans and to get a goal for them, I'm really happy.
"Training with the lads day-in, day-out is really beneficial. You try to take everything on board and take it into situations like tonight."
Crystal Palace manager Alan Pardew:
"Shane Long is quick and has got a bit of history in those situations. He was definitely going over, I know that, but the video I saw was inconclusive.
"The players felt it (the penalty) was a bit harsh but it was difficult to see unless you see it clearly on television.
"The best team won for sure. They were very sharp. Their passing and movement caused us problems.
"It is always a risk when you make a lot of changes and we had one or two players that looked a bit rusty. We didn't have enough imagination to find a route to goal."
Match ends, Southampton 2, Crystal Palace 0.
Second Half ends, Southampton 2, Crystal Palace 0.
Offside, Crystal Palace. Joel Ward tries a through ball, but Christian Benteke is caught offside.
Corner,  Southampton. Conceded by Wayne Hennessey.
Attempt saved. Nathan Redmond (Southampton) right footed shot from outside the box is saved in the bottom right corner. Assisted by Matt Targett.
Christian Benteke (Crystal Palace) wins a free kick on the left wing.
Foul by José Fonte (Southampton).
Foul by Joel Ward (Crystal Palace).
Jordy Clasie (Southampton) wins a free kick in the defensive half.
Substitution, Southampton. Dusan Tadic replaces Shane Long.
Wilfried Zaha (Crystal Palace) wins a free kick on the right wing.
Foul by Harrison Reed (Southampton).
Yohan Cabaye (Crystal Palace) is shown the yellow card for a bad foul.
Foul by Yohan Cabaye (Crystal Palace).
Nathan Redmond (Southampton) wins a free kick in the attacking half.
Attempt missed. Yohan Cabaye (Crystal Palace) right footed shot from outside the box is high and wide to the left.
Attempt saved. Christian Benteke (Crystal Palace) header from the centre of the box is saved in the centre of the goal. Assisted by Wilfried Zaha with a cross.
Lee Chung-yong (Crystal Palace) wins a free kick in the defensive half.
Foul by Shane Long (Southampton).
Matt Targett (Southampton) is shown the yellow card for a bad foul.
Wilfried Zaha (Crystal Palace) wins a free kick on the right wing.
Foul by Matt Targett (Southampton).
Substitution, Southampton. Pierre-Emile Højbjerg replaces Jake Hesketh.
Delay over. They are ready to continue.
Delay in match Maya Yoshida (Southampton) because of an injury.
Delay over. They are ready to continue.
Substitution, Crystal Palace. Jason Puncheon replaces Jordon Mutch.
Delay in match José Fonte (Southampton) because of an injury.
Yohan Cabaye (Crystal Palace) wins a free kick in the defensive half.
Foul by James Ward-Prowse (Southampton).
Attempt saved. Jake Hesketh (Southampton) left footed shot from outside the box is saved in the centre of the goal. Assisted by Nathan Redmond.
Substitution, Crystal Palace. Christian Benteke replaces Bakary Sako.
Goal!  Southampton 2, Crystal Palace 0. Jake Hesketh (Southampton) left footed shot from the centre of the box to the top right corner.
Attempt saved. Shane Long (Southampton) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by James Ward-Prowse.
Attempt missed. Matt Targett (Southampton) left footed shot from outside the box misses to the right following a corner.
Corner,  Southampton. Conceded by Damien Delaney.
Connor Wickham (Crystal Palace) wins a free kick in the attacking half.
Foul by Maya Yoshida (Southampton).
Substitution, Southampton. Nathan Redmond replaces Charlie Austin.
Jordon Mutch (Crystal Palace) wins a free kick in the defensive half.
Southampton made light work of Crystal Palace in their all-Premier League tie, with a goal in either half sending Saints into the EFL Cup fourth round.