The Magpies were not their incisive selves during the first half and Ruben Selles's Saints went into the break ahead thanks to Stuart Armstrong's goal following a breathtaking counter attack.
Eddie Howe made alterations during the half-time interval and saw his Europe-chasing men dominant the second-half proceedings, with a brace from Callum Wilson and an own goal from Theo Walcott securing a maximum for the Geordies.
The visiting Saints started the game in promising fashion at a sold-out St James Park, but it was Newcastle who had the first massive chance of the contest, with Anthony Gordon close to putting his side ahead.
Alexander Isak picked up the ball in midfield and sent the ex-Everton youngster through on goal with a defence-splitting pass, however Gordon's one-on-one effort struck the outside of Alex McCarthy's post.
The in-form Jacob Murphy then went close for the Magpies with a curling effort from just outside the box - Howe's men were beginning to assert their dominance on proceedings in the North East.
Despite Newcastle having most of the ball and keeping Southampton limited to fleeting moments of attack, a brilliant tackle from highly-rated Romeo Lavia kick-started a fast break which would give the strugglers an unlikely lead.
The Belgian international dispossessed Bruno Guimaraes in the middle of the park and sent Carlos Alcaraz driving up the pitch who then fed the ball out to the dangerous Kamaldeen Sulemana.
Having created some space for a cross, the Ghanaian delivered a wicked ball across the Newcastle penalty area and Armstrong raced ahead of Kieran Trippier to bundle in his second of the Premier League campaign.
England international Wilson entered the field at half time in place of Gordon and was quick to get his side back on level terms when he directed an Isak cross past McCarthy in the Saints net.
The 31-year-old - and the entirety of the home support - thought Newcastle's comeback had been completed when Wilson finished once again from close distance, however the ball was adjudged to have come off Miguel Almiron before reaching the striker, who was in an offside position.
Southampton continued to struggle amid waves of Newcastle pressure and their resistance crumbled away in the space of two minutes - a spell which would mean the Saints left the North East with no points.
Sven Botman managed to flick on the ball after a corner kick and it fell to Walcott in the box, with the ex-Arsenal man making awful work of his clearance which he sliced into his own net - to the absolute dismay of his teammates.
Things got even worse for the Premier League's bottom side soon after, with Ainsley Maitland-Niles and Jan Bednarek both failing to deal with a hopeful long ball - in truth it was calamitous defending which allowed Wilson to round McCarthy and secure a second-half brace.
Next up for Newcastle is a home clash with title-chasing Arsenal next Sunday, whilst Southampton have to wait eight days until they can try to respond with a result against relegation rivals Nottingham Forest at the City Ground.