Greg Taylor fired a low finish beyond Jon McLaughlin shortly after the hour to hand Celtic the lead, before substitute Scott Arfield bent home a brilliant leveller to force additional time.
With a penalty shoot-out on the horizon, Starfelt deflected Calvin Bassey's left-wing cross past Joe Hart to send Rangers to their 53rd Scottish Cup final, where Hearts lie in wait after overcoming Hibernian on Saturday.
A boisterous atmosphere gave way to a frantic opening at Hampden Park, with Ryan Kent firing over under pressure and Jota heading onto the roof of the net at the other end.
John Lundstram curled against the post as Rangers enjoyed the better of the first half, but their threat faded somewhat after Aaron Ramsey was injured shortly before the break.
Ange Postecoglou's side improved after half time and took the lead after 63 minutes, Taylor spinning on Callum McGregor's inventive shot free-kick before firing into the bottom-right corner.
The Hoops went close to a quickfire second five minutes later when Cameron Carter-Vickers crashed a left-footed shot against the crossbar from a corner.
They were made to pay for that missed opportunity after 78 minutes with Arfield latching onto Kemar Roofe's heavy touch to curl home just four minutes after coming on.
Celtic somehow survived Rangers twice hitting the woodwork in the 110th minute, James Tavernier smashing off the near post and Fashion Sakala diverting the rebound onto the top of the bar.
But Rangers found time for a winner as Bassey's left-wing cutback was diverted into his own net by Starfelt under pressure from Sakala, ending Celtic's treble hopes and booking Rangers' cup final spot.
What does it mean? Rangers continue bid to end cup draught
Rangers have not lifted either of Scotland's two domestic cups since winning the Scottish League Cup in 2011, and Celtic have won the Scottish Cup on six occasions since the Ibrox outfit last did so in 2009.
Their extra-time win means they will appear in May's showpiece event for the 53rd time, where they will look to lift their first domestic cup in over a decade.
Celtic's treble hopes in tatters
Meanwhile, Celtic went into this game looking to keep their hopes of a fifth domestic treble in six seasons alive, after winning the Scottish League Cup in December and establishing a six-point lead at the top of the Scottish Premiership.
Giovanni van Bronckhorst's men will be delighted with ending the Hoops' dreams of another domestic clean sweep, and could yet win two trophies themselves as they remain in the hunt for the Europa League.
Gers end Postecoglou's derby run
Postecoglou's team looked set for a third successive Old Firm derby win when Taylor fired home the opener, but a stunning Rangers turnaround denied Celtic that feat, and means the Glasgow giants have won two derbies apiece in all competitions this season.
What's next?
Celtic continue their bid to regain the Scottish title at Ross County next Sunday, with Rangers travelling to Motherwell on the same day, looking to capitalise on any slip-up from the leaders.
Abada was in superb form as he helped fire the hosts to a sixth successive victory of the Scottish Premiership season, with Jota and David Turnbull also on the scoresheet at Celtic Park.
The win moved Ange Postecoglou's side five points clear at the top ahead of their Champions League meeting with Real Madrid next week.
For Giovanni van Bronckhorst's visitors however, it laid bare the gulf in quality, and checks the Gers' momentum before their midweek trip to Ajax.
Celtic had to recover from an early blow when Kyogo Furuhashi, the league's top scorer, was forced off clutching his shoulder following a collision with John Lundstram.
Yet those early fears turned to joy when Celtic seized the first chance of the game – Abada turning Matt O'Riley's cross in off Jon McLaughlin's palm with a lunging volley.
O'Riley provided again for the Bhoys to double the lead, with a superb ball for Jota, who turned home sharply, and Celtic's fans were in dreamland when Abada doubled his tally with a first-touch finish from six yards out.
With a three-goal deficit to overturn after the break, Rangers had to make some kind of change, with Scott Wright thrown on for Glen Kamara, but that gamble failed to stem the Celtic onslaught.
Celtic seldom let their foot off the pedal, and when McLaughlin played a short goal-kick straight to Turnbull, an easy finish sealed the deal for the hosts in emphatic, dominant fashion.
What does it mean? Celtic cement frontrunner status
Twenty-five goals in the space of six league games is not just an impressive haul, it is positively confirmatory for Celtic's title hopes, even at this early stage.
Even before their free-scoring performance in the derby, they had not netted as many goals as they had by this stage of any previous SPL season. They look impossible to stop.
Bhoys buck bad starts
The first league Old Firm derby of a season has been won by Rangers in both of the last two campaigns. Before that, Celtic had won four in a row – and now they have shaken off the slow form that has cost them the past two years.
Van Bronckhorst makes unwanted history
Rangers are yet to win an Old Firm league derby under the Dutchman. It makes him the fourth such man to fail to register a win in his first four encounters, after William Wilton in 1892, William Waddell in 1971 and Graeme Murty in 2018.
What's next?
Both teams enter the Champions League group stages against two European heavyweights, with Celtic welcoming Madrid and Rangers travelling to Ajax.
The England winger has only made three Premier League starts this season.
Sterling, who starred during England's run to the Euro 2020 final, could now be on the move.
TOP STORY – BARCA RESOLUTE ON RAHEEM
Barcelona are determined to sign Raheem Sterling from Manchester City despite the Premier League club's refusal to let him leave, reports Manchester Evening News.
The Catalans want to bring Sterling to Camp Nou in January on a loan deal, with the forward open to a move after losing his regular starting spot at City.
Sterling still has 18 months remaining on his City contract and the English champions have no intention of accepting an offer for him.
ROUND-UP
- Manchester City are set to launch a new bid for Tottenham forward Harry Kane in January, claims ESPN. City pursued Kane over the off-season but the Spurs skipper ultimately remained in London after Tottenham declined their approaches.
- El Nacional reports Real Madrid head coach Carlo Ancelotti has told the club to sell or release Gareth Bale. The Wales forward has only made three appearances this term and is contracted to Los Blancos only until the end of the season.
- Hakim Ziyech is unhappy at Chelsea and could be lured to Borussia Dortmund, claims The Mirror. The Morocco winger could move in January, having been unable to re-discover his best form at Chelsea after moving from Ajax in 2020.
- Norwich City are set to offer ex-Aston Villa boss Dean Smith their vacant manager role, according to Sky Sports. Smith was sacked as Villa coach this week.
- The Daily Record claims former Feyenoord coach Giovanni van Bronckhorst will hold talks with Rangers about taking over as manager after Steven Gerrard's departure for Villa.
