Miguel Almirón's composed finish, the Paraguayan's seventh goal in as many Premier League matches, opened the scoring at St Mary's Stadium before Chris Wood, replacing Callum Wilson at the half-time break, doubled the visitors' advantage before the hour-mark with a bending effort.
Joe Willock's first goal of the season, racing onto Kieran Trippier's delightful through ball, added gloss to the scoreline and despite Romain Perraud's late strike denying United a seventh clean sheet of the season, Bruno Guimarães' curling stoppage-time effort sealed another emphatic victory for Eddie Howe's side.
Eddie Howe made one change to the starting eleven which claimed an impressive 4-0 home win against Aston Villa last week as Jacob Murphy replaced Joelinton, with the Brazilian serving a one-match suspension after picking up a fifth yellow card of the season against the Villans.
The Magpies created the opening opportunity in front of goal as Willock swept the ball into Sean Longstaff's path before the latter's inviting cross from the right wing almost found Wilson inside the penalty area, with the in-form striker inches away from connecting with the ball.
Nick Pope, targeting a seventh clean sheet of the season, kept the visitors on level terms after pushing away Romain Perraud's low drive from the edge of the box after the Frenchman cut dangerously inside from the left flank.
In the 35th minute, Newcastle took the lead as Almirón continued his electrifying form in front of goal. After neat build-up play consisting of Longstaff and Wilson, the South American forward darted towards goal, evading the challenge of Ainsley Maitland-Niles before slotting the ball beyond Gavin Bazunu.
Longstaff was unfortunate not to double Newcastle's lead as the central midfielder connected with Willock's cross from the left byline, following impressive link-up play with Jacob Murphy, but saw his brave header fly over the crossbar.
On the stroke of half-time, Newcastle were fortunate to remain on level terms as Mohamed Elyounoussi latched onto Stuart Armstrong's dangerous low pass at the back post but failed to convert from close-range as his wild strike flashed past the target.
Newcastle began the second-half without the services of Wilson as the Coventry-born striker was replaced by Wood, who scored his first goal for Newcastle during last season's 2-1 away win against Southampton.
After Southampton threatened in the opening stages of the restart, it was Wood who extended Newcastle's lead in the 58th minute, the New Zealand international's first Premier League goal of the 2022/23 campaign.
After Murphy managed to pick out Wood inside the box, the physical striker guided a right-footed effort into the far right-hand corner.
Four minutes later, Newcastle found themselves further ahead as Willock netted United's third of the afternoon, the midfielder's first Magpies goal since February.
After Trippier controlled a loose ball, the Newcastle captain threaded a wonderful pass into Willock's path, who raced in-behind the Saints backline before firing the ball into the bottom right-hand corner.
Pope thought he had kept Newcastle's clean sheet hopes on course in the final minutes after tipping over Mohamed Salisu's header following James Ward-Prowse's teasing corner.
However, in the 89th minute, Southampton pulled one back through Perraud as the left-back latched onto Maitland-Niles' pass and after advancing beyond Dan Burn, curled the ball into the top right-hand corner.
Newcastle, though, reclaimed their three-goal advantage as Guimarães, who netted on his full Newcastle debut against Southampton last term, scored in the first minute of stoppage-time.
After exchanging passes with substitute Allan Saint-Maximin, the Brazilian midfielder placed the ball into the bottom right-hand corner from the edge of the penalty area, recording his third league goal of the 2022/23 campaign in the process.
