The former Buffs and Ardeer Thistle man struck the opening goal as the Championship side shocked the Premier League leaders in their quarter-final clash on Saturday.
The Scotland international - who will be hoping to catch the eye of Steve Clarke ahead of this summer's World Cup - struck home on 35 minutes to put the Saints ahead.
It was the striker's second consecutive FA Cup goal after notching the winner as Southampton dumped out Premier League club Fulham in the previous round.
Despite Viktor Gyökeres levelling the tie on 68 minutes, it was the Championship club who found the winner as Shea Charles slotted home with five minutes remaining.
They will now head to Wembley on Saturday, April 25, to take on Manchester City for a place in the competition's final.
Stewart will be hoping to maintain his impressive record at the English national stadium - having been on the winning side in his two previous visits there.
(Image: Steven Paston/PA Wire)
The North Ayrshire attacker scored in a 2-0 League One play-off final win with Sunderland back in 2022 though was an unused substitute when his current team earned promotion to the Premier League in the Championship play-off showpiece in 2024.
“I’m really relishing it,” he said via the Southampton website. “The semi-final of the FA Cup doesn’t come along for every player, and it’ll certainly be my first taste of it.
“Obviously I’ve been to Wembley a couple of times. With Saints it probably wasn’t how I would’ve pictured it – I wasn’t involved and didn’t feel as part of it through injuries – but the time before that with Sunderland I felt very part of it.
“Regardless of whether I’m part of it or not, I hope we go there and win. I’m desperate to be involved, I want to be involved, I love playing the big occasions and there’s no bigger than Wembley.
“Hopefully I can go there and continue this wee scoring streak that I’m on in this cup, but between now and then it’s fully focused on league business, and hopefully I can score a few goals between now and then too.”