Saints goalkeeper Bartosz Bialkowski and on-loan Reading defender Alan Bennett played their part in all four goals for Palace.
Scowcroft opened the scoring on 30 minutes with a free header from Tony Craig's corner.
Republic of Ireland international Bennett was meant to be marking Scowcroft, but lost him completely as he headed home from six yards.
Scowcroft doubled his side's advantage within a minute when Bennett failed to deal with a long clearance from Palace goalkeeper, Julian Speroni.
Scowcroft shrugged off the feeble challenge of Bennett and lobbed the ball over the stranded Bialkowski from 25 yards.
Saints managed to get a goal back before the break through Polish striker Marek Saganowski.
Midfielder, Andrew Surman put over a teasing centre and Saganowski fired home from 12 yards via the underside of the crossbar.
Bialkowski then made an absolute howler when he handed a long clearance straight down to the feet of Scowcroft. The hitman made no mistake as he slotted the ball home from 20 yards.
Strike partner, Clinton Morrison, added a fourth on 57 minutes after Bennett failed to get in a challenge.
Ex-Republic of Ireland international striker Morrison made no mistake as he powered the ball home with a right-footed shot into the bottom left-hand corner.
Shell-shocked Saints were all at sea as the Palace fans were absolutely delirious. An angry Saints fan ran on to the pitch and threw his season ticket down to the ground in disgust as he was led away by three police officers.
Surman and Grzegorz Rasiak both went close to pulling a goal for Southampton, but found Argentinian Speroni in inspired form in the Palace goal.