Celtic's Carl Starfelt put through his own net deep into extra-time as Rangers came from behind to beat their Old Firm rivals 2-1 in a frantic Scottish Cup semi-final.

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.