The manager's team ended a run of six successive defeats that had put intense pressure on his position while earning their first clean sheet since August after two goals from Christian Benteke and another from James Tomkins.
Victory took them away from the relegation zone while Southampton slid to 11th after a flat performance - and came after a week in which Pardew drilled his defence at Selhurst Park instead of their Beckenham training ground and did additional work to improve their set-pieces.
Damien Delaney excelled in central defence after being recalled while Joel Ward was comfortable after switching to Palace's problem left-back position, but Pardew said the composed performance they produced was in contrast to that seen in training.
"We had a session on Thursday that was the complete opposite," said Pardew, who was reportedly at risk of the sack if Palace lost a seventh straight game
"Sometimes you need that on the training ground.
"You've got frustration: we were tight, giving the ball away in our team play.
"Defensively we had to be sound, there was no other box we needed to tick: that was the most important one
Set-plays we were calm.
"I always think as a manager at any level, particularly in the modern era: expect the sack
Just expect it; it's coming at some stage, so just do your job as best you can
Every week, that's what I try to do.
"It was an important message to give the players after
The six defeats we've had, the way we've played, we didn't deserve what we got, but we needed to put that right.
"Damo (Delaney) is a leader
He's not blessed with massive amounts of talent but he makes up for it with his personality, desire and leadership, and we got all of that from him.
"The back four was better for him in it
They needed defensive work
They longed for it; they wanted the clean sheet.
"We really were hurt by the Swansea game (losing 5-4 last week after conceding two late goals), and you saw that hurt.
"Next week at Hull is even more important
We can't afford to lose that; we must go up there and get something."
Palace took the lead in the 33rd minute when Southampton goalkeeper Fraser Forster inexplicably missed the ball at an attempted clearance, gifting Benteke the easiest of tap-ins on the striker's 26th birthday.
Further poor defending teed up Tomkins for another close-range finish just three minutes later, before Benteke's 85th-minute goal secured all three points.
Southampton were unexpectedly poor while pursuing their third victory in a week, but their manager Claude Puel insisted Forster was not to blame and that his team struggled because of the Selhurst Park pitch.
"For me it's the bad pitch and it was difficult to play in the second half, for example, against a team two goals up," the Frenchman said
"It was difficult to find a good solution and to put good play on this pitch.
"It is not the fault of Fraser.
"It was the bad pitch (that) gives opportunities to the opponent."
Source : PA
Source: PA