Rangers stunned Old Firm rivals Celtic 5-4 on penalties after a pulsating 2-2 draw at Hampden Park to book their place in the Scottish Cup final, with Tom Rogic missing the decisive spot-kick.

Former Celtic striker Kenny Miller gave Rangers the lead after 15 minutes on Sunday, scoring an instinctive finish after Hoops captain Scott Brown deflected a cross into his path.

Patrick Roberts spurned a golden opportunity to level the scores, hitting the side netting with the goal wide open, but Celtic equalised shortly after half-time through Eric Sviatchenko.

The substitute got up highest to head in a Roberts corner after 49 minutes and Leigh Griffiths wasted a good chance by shooting off-target as the game drifted into extra-time.

Barrie McKay drew first blood in the added period, turning into a pocket of space 25 yards out and arrowing an unstoppable drive into the top-right corner, but Rogic tucked in a second Celtic equaliser from Kieran Tierney's low cross.

Griffiths almost won it in the final stages of extra-time, but his long-range free-kick cannoned off the woodwork.

After both teams had netted four of their first six penalties, it was Rogic who followed up Nicky Law's calm finish by blazing his kick well over the crossbar in to spark wild celebrations from Rangers' half of the Hampden crowd.

Mark Warburton's side - who were recently promoted back to the Scottish Premiership for next season - will face fellow Championship side Hibernian in the final after they beat Dundee United 4-2 on penalties following a 0-0 draw in Saturday's semi-final.