After finding themselves 1-0 and 2-1 behind, a stoppage-time winner from Scott McTominay ensured that Steve Clarke's side took a step closer to qualification for the 2022 World Cup with a 3-2 victory.
Aston Villa midfielder John McGinn cancelled out Eran Zahavi's early opener in the 29th minute, before Munas Dabbur restored the visitors' lead in the first-half.
Queens Park Rangers striker Lyndon Dykes then levelled again after the break, making up for his earlier tame penalty miss, with McTominay appearing at the back post from a late corner to nudge in the winning goal on the line.
The Hampden Park crowd, who were probably expecting the worst when their team twice went behind, emphatically celebrated the last-minute goal.
And, just like they did throughout Euro 2020, the home fans belted out a rendition of 'Yes Sir, I Can Boogie' as the full-time whistle was blown.
A video posted on social media shows the Scotland squad parading around the pitch, as the crowd belts out their new unofficial anthem.
The players - including goalscorer McTominay, Liverpool star Andy Robertson, 19-year-old Rangers ace Nathan Patterson and Bournemouth's Ryan Christie - seemed to be enjoying the sing-song as much as the supporters.
And Tartan Army boss, Clarke, says the fans were a massive part of their comeback in Glasgow.
He said: "It was a great way to finish the game and you see the atmosphere in the crowd.
"We can enjoy ourselves, but not too much because that is one of the cup finals out of the way, now we have to dust ourselves down and go against the Faroes.
"It gives us a bit more belief going forwards, but I keep saying about this group of players - they show it every time they go onto the pitch.
"They want to be successful for their country, and that is what the second half was all about."
Whilst Manchester United's McTominay got himself on the scoresheet, it was Liverpool's Robertson who was Scotland's star man, with the left-back providing assists for two of Scotland's three goals.
Chelsea's Billy Gilmour, on loan for the season at Norwich, also impressed, as the 20-year-old stepped up when his team needed him in the second half.
Scotland now face the Faroe Islands on Tuesday, as they look to build on their phenomenal win on Saturday night and edge even closer to a play-off place.