A capacity crowd at St. James' Park saw Eddie Howe's side beat the Saints 2-1 on the night as the Premier League high-flyers continued their fantastic season.
Sean Longstaff was the local hero as the boyhood Newcastle fan scored twice inside 20 minutes to give Southampton an uphill task away from home.
Che Adams's wonder goal just before the half-hour mark made the tie interesting but Southampton struggled to make much of an impact on the game as Newcastle's eased to victory.
Newcastle now have a first cup final to look forward to since the FA Cup final in 1999, where they will face either Manchester United or Nottingham Forest to try to end a 68-year wait for a major honour.
Having not been in FA Cup action at the weekend, Newcastle had the luxury of naming a fully-fresh, unchanged starting XI from the side that won 1-0 at St. Mary's last Tuesday, and they flew out of the traps in the early stages.
It took the Magpies just five minutes to open up the visitors, as Kieran Trippier laid the ball off for an on-rushing Longstaff who swept a shot beyond Gavin Bazunu in the Southampton goal to make it 1-0.
That opened up a two-goal lead on aggregate and they soon made it a two-goal lead on the night too, when a swift counter down the left-hand side saw Miguel Almiron deliver a low cross for Longstaff to run onto once again and fire home.
It was a remarkable feat for the midfielder who is not a usual source of goals, as he scored more goals in the opening quarter of this match than he had done in all of his previous 60 matches at St. James' Park, where he had only one which came in February 2019.
It could easily have been a hattrick too as another adventurous run from midfield saw the ball fall for him near the penalty spot, just minutes after his first goal, but he sent the effort narrowly wide.
Newcastle were relentless for the first 25 minutes and Southampton could not handle them as they prised open their midfield and defence time and time again.
Carlos Alcaraz and Lyanco were two that particularly struggled to cope with the tempo of Newcastle's attacking play, and unsurprisingly were both replaced by manager Nathan Jones at half-time.
They went in at half-time still in the tie though, thanks to a bolt from the blue from Adams, who latched onto a loose pass from Joe Willock to fire beyond Nick Pope from 25 yards out.
However, the game continued in a similar pattern to how it started and Newcastle remained the only side who looked likely to score next.
The second half quickly turned into a drab affair with Newcastle possibly a little too relaxed and complacent, but the Saints struggled to impose themselves in the final third.
Adam Armstrong could have done better when Romeo Lavia threaded an excellent ball through the heart of the Newcastle back four, but the former Magpie fired straight at Pope.
Longstaff went close to a hat-trick again and Bruno Guimaraes grazed the outside of the left-hand post in the latter stages, but in a shock twist, the Brazilian was then sent off shortly after for a dangerous challenge on Samuel Edozie.
James Ward-Prowse could not beat the wall from the resulting free kick though, and it remained 2-1 on the night as the hosts comfortably progressed.
With Manchester United 3-0 up from their respective first leg away to Nottingham Forest, it looks like it will be a repeat of Newcastle's last cup final, when the Red Devils won 2-0 to claim a 10th FA Cup crown in 1999.
Many generations have passed since Newcastle last lifted silverware, as the 1955 FA Cup final was the last occasion in which they tasted success, and with the form they are in, they go into the final with a huge chance of ending all those years of hurt.
Despite their exit tonight, there is still cup interest for Southampton this season, as they remain in the FA Cup, and will face Luton Town or Grimsby Town in the fifth round in a months' time.
With Southampton sitting bottom of the Premier League, their task for February will be solely to try to move out of the bottom three, and they travel to Brentford on Saturday, just two points from safety.