It is still all to play for in the second leg, which takes place next Tuesday, but it will now be a huge ask for Southampton to reach Wembley, given that Newcastle are unbeaten at home all season.
It was a bright start from Eddie Howe's side, pinning Southampton back in the defensive third, with Miguel Almiron and Matty Longstaff looking lively and putting balls into dangerous areas, but nobody was able to get on the receiving end and threaten Gavin Bazunu.
The Magpies have a fantastic defensive record this season, keeping clean sheets in seven of their last eight matches, and they looked solid at the back throughout the first half, with the Saints struggling to craft any real opportunities.
There was not too much attacking threat posed by the visitors, having to mainly settle for half-chances from set plays and crosses, but Joe Willock spurned a fantastic opportunity on the 35-minute mark, firing way over the bar after a pinpoint Kieran Trippier cross.
As the game edged closer towards half-time, there was a moment of controversy when Joelinton had the ball in the back of the net after following up a parried effort from Willock, with the goal being ruled out for an apparent handball from the Brazilian in the build-up.
Despite Howe's side looking the more lively, it was the Saints who recorded the only shot on target in the opening 45 minutes, although it was a tame effort, with Carlos Alcaraz firing a long-range effort straight at Nick Pope, causing the goalkeeper no issue.
Almiron continued to threaten the Southampton backline in the second half, and he created a golden opportunity for Joelinton in the early stages, but the 26-year-old fluffed his lines, somehow firing over the bar from just six yards out.
As the game wore on, Nathan Jones's side upped the tempo, perhaps sensing that a draw would not be enough to take to St James' Park in the second leg, but Che Adams failed to convert two great chances that came his way, being denied by a smart save from Pope with his second attempt.
Just as the Saints appeared to be gaining a foothold in the game, Newcastle came to life down the other end, with Alexander Isak doing brilliantly to work some space down the right, before picking out Joelinton, who made no mistake from six yards out this time, firing his side into the lead.
After Newcastle had a goal ruled out for handball in the first half, it was Southampton's turn just minutes after the visitors opened the scoring, when Adam Armstrong scrambled the ball home against his former club, but it was correctly ruled out after a VAR check.
There were some indications that the hosts were going to make it a nervy finish for the Magpies by piling the pressure on in the latter stages, but the visitors' task got easier when Duje Caleta-Car saw red for a second bookable offence after a foul on Allan Saint-Maximin, and they held on for a 1-0 victory.
Newcastle now have a fantastic chance of reaching the final of the EFL Cup, and competing to win a major honour for the first time in 54 years.