A first-half penalty from Charlie Austin opened the scoring after Shane Long had been brought down by substitute Martin Kelly in the penalty area.
Jake Hesketh then doubled his side's lead with his first senior goal, rifling home after Wayne Hennessey did well to save Long's initial shot.
Dann hobbles off injured for Palace
Eagles captain Scott Dann was withdrawn after just 18 minutes for the visitors, appearing to be clutching his hamstring as he retreated to defend a Saints counter-attack.
This is a huge worry for Alan Pardew who saw fellow central defender James Tomkins forced off with a knee injury midway through their victory against Stoke City at the weekend.
Dann's replacement, Kelly, came on in his preferred centre-back position, although had a strong hand in the hosts taking the lead. Cuco Martina's cross was cut out by Kelly but the former Liverpool defender dithered, allowing Long to sneak in and win the ball before being brought down by the defender.
Austin sent Hennessey the wrong way from the spot, although it could be argued that neither side deserved to had into half-time in front.
The Eagles had struggled to get into the game with the returning Connor Wickham offered very little support by a midfield that lacked urgency and mobility. The Saints' style starkly contrasted and their movement was just too much for Palace in the opening period.
Saints secure win in drab second half
Both sides improved in the second half, but chances were still at a mere minimum. Damien Delaney had Palace's first effort of the half but his shot was dragged well wide of the post.
Yohan Cabaye, returning from injury, then had a chance to equalise but his shot was straight at former Eagles goalkeeper Alex McCarthy who was playing his first competitive game for his new side.
Southampton's academy is renowned for producing excellent talent; there were no less than four starters who had come through their youth ranks. Attacking midfielder Hesketh appears to be the next to follow in the footsteps of Luke Shaw, Calum Chambers, Matt Targett and James Ward-Prowse of recent times and capped a fine performance with a goal just past the hour mark.
Long was given an easy route in behind the makeshift Palace back four but saw his intial shot saved by Hennessey. However, a lack of reaction from two Eagles players allowed room for Hesketh to strike the ball into the top corner with a left-footed drive.
Cup draw sees Saints paired with Sunderland
The victory put Southampton into the draw or the third round, which took place straight after full-time. Claude Puel's side have been given another all-Premier League home tie, this time against struggling Sunderland.
Meanwhile, Crystal Palace - who reached the fourth round last year - will be allowed to concentrate on their top-flight fixtures until the FA Cup third round begins in January. The Eagles also face Sunderland on Saturday in the Premier League.