Schar was handed a straight red card in the 28th minute of the contest following a clash of heads with Southampton's Ben Brereton Diaz, but Newcastle managed to take the lead in the closing stages of the first period through Joelinton.
A mistake from Southampton goalkeeper Alex McCarthy led to Alexander Isak crossing into Joelinton, who found the bottom corner to make the breakthrough at St James' Park, and the Brazilian's effort proved to be the difference between the two sides.
Newcastle have now won their last six games against Southampton in all competitions, and it was the perfect start for a Magpies side that will be looking to secure a return to European football for the 2025-26 campaign.
Southampton, who were promoted from the Championship last season via the playoffs, dominated the possession (75%) against Eddie Howe's side, while they had 18 attempts, including six on target, with the Saints putting the pressure on their 10-man opponents.
However, Newcastle, backed by a vocal home support, held firm in a defensive area and were able to navigate their way to a one-goal win on Saturday afternoon, finding the back of the net from their only shot on target.
NEWCASTLE VS. SOUTHAMPTON HIGHLIGHTS
28th min: Newcastle 0-0 Southampton (Fabian Schar red card)
Newcastle are reduced to 10 men in the 28th minute of the contest, as Schar is handed a straight red card for an apparent headbutt on Brereton Diaz.
Schar nudged his head towards Brereton Diaz after a heavy challenge from the Southampton attacker, and the centre-back is handed a straight red card.
VAR agreed with the referee, but it was a slightly controversial call.
45th min: GOAL! Newcastle 1-0 Southampton (Joelinton)
Newcastle, despite being down to 10 men, make the breakthrough in the 45th minute of the contest, with Joelinton collecting a low cross from Isak before picking out the bottom corner.
A poor pass from Southampton goalkeeper McCarthy put his team in trouble, and it was a clever assist from Isak, with Joelinton finishing for 1-0.
MAN OF THE MATCH - JOELINTON
Joelinton was the star of the show for Newcastle on Saturday afternoon, with the Brazilian putting in a brilliant all-round performance at St James' Park.
It was the midfielder's clever finish that made the breakthrough, while he won four aerial duels and put in a lot of running to make up for the extra man.
The 28-year-old only scored two Premier League goals last season, but he is already off the mark for the new campaign, and his passion was crucial for the Magpies.
NEWCASTLE VS. SOUTHAMPTON MATCH STATS
Possession: Newcastle 25%-75% Southampton
Shots: Newcastle 4-18 Southampton
Shots on target: Newcastle 1-6 Southampton
Corners: Newcastle 3-12 Southampton
Fouls: Newcastle 14-14 Southampton
WHAT NEXT?
Newcastle will be bidding to make it successive wins at the start of the new Premier League campaign when they head to Bournemouth on August 25.
However, the Magpies will be without the services of Schar, with the centre-back set to miss his side's next three games in all competitions, unless an appeal is successful.
Southampton, meanwhile, will be aiming to bounce back from their opening-weekend setback when they welcome Nottingham Forest on August 24.