Pelle opened the scoring after just six minutes, nodding home a cross from Ryan Bertrand which left Newcastle goalkeeper Tim Krul with no chance.
Five minutes later, the Saints doubled their lead when the former Feyenoord striker tapped the ball into an empty net following some unselfish work from Dusan Tadic.
Less than ten minutes into the second half, Southampton added a third when Jack Cork capitalised on a defensive mix-up between Mike Williamson and Krul, gifting the midfielder the opportunity to stroke the ball into an open goal.
In stoppage time, Morgan Schneiderlin picked up the ball in the Newcastle area and curled a sumptuous effort beyond a sprawling Krul to make it 4-0, compounding a miserable afternoon for the travelling Toon Army.
The result secures Ronald Koeman’s second Premier League win as Southampton boss, but in stark contrast, Pardew’s future at Newcastle looks decidedly uncertain after his side’s awful performance on the south coast leaves them bottom of the Premier League.
A recent poll showed 85 per cent of supporters did not want the Magpies manager to stay, and those dissenting voices were given further ammo by a tepid performance at St Mary’s.
An angry fan had to be apprehended after running on to the pitch at the end of a game which looked to be going only one way after just 23 seconds.
Attempting to clear a Fabricio Coloccini backpass, Krul’s clearance struck Shane Long but, fortunately for the Newcastle goalkeeper, went wide.
It was a warning shot the visitors failed to heed as, after some last-ditch challenges and a penalty appeal from Long, Saints opened the scoring after six minutes.
Meeting a Bertrand cross from the left, Pelle, the man charged with replacing talisman Rickie Lambert, impressively powered a header into the top left-hand corner.
The Italian was clearly keen to add to his tally and showed impressive inventiveness to hook goalwards from an acute angle, forcing an unorthodox save from Krul.
Pelle’s second eventually came in the 19th minute, though, courtesy of his own miscued strike. The 29-year-old attempted to volley a Williamson clearance but it went so wide it landed at the feet of Tadic, who ignored offside appeals to square the ball for the frontman to tap home.
“We want Pardew out” soon echoed around St Mary’s, with both sets of fans chanting “you’re getting sacked in the morning”.
It took 26 minutes for Newcastle to call their former goalkeeper into action and when they did Fraser Forster showed why Saints forked out £10million for his services, denying a close-range, first-time Moussa Sissoko effort.
The England international also had to be alert to a fizzing Jack Colback drive as United improved towards the end of the first half, although a deflected Yoan Gouffran effort was the only chance of note they could muster.
Cork scored in the recent Capital One Cup tie at Millwall but had failed to net a league goal for Saints over two spells with the club until latching on to a deflected Steven Davis ball, rounding Krul and slotting home.
It was a period in which the visitors came close to scoring on several occasions, with Emmanuel Riviere and Colback somehow failing to turn home before Forster denied a Gouffran header.
Florin Gardos joined fellow debutant Toby Alderweireld for the final few minutes, which saw Schneiderlin add extra gloss with a wonderful curling effort in stoppage time.
Alan McInally on Southampton v Newcastle
Alan Pardew will be punch drunk after watching that. Riviere, Cabella, Janmaat, Gouffran, Anita, the two centre-halves… they were all bang average. Like the Newcastle fans we always think Newcastle are going to be better and they haven’t been. Alan has been banging his head and I know a lot of fans want him out. The way they played today is relegation candidates, big time. There seemed to be no real urgency.
I’m talking about fight within a football team, I’m talking about personalities that say ‘hey, come on’. Cheick Tiote came on and has got more about him, but he isn’t going to be enough to keep Newcastle in the division. It will all depend on what Mike Ashley wants to do. On the bare-faced stats, there have been managers sacked for less. They were so poor, as poor as I’ve ever seen a Newcastle team.