Rangers have defeated Old Firm rivals Celtic in a nail-biting penalty shootout at Hampden Park to reach the final of the Scottish Cup.

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Celtic's Tom Rogic went from hero to villain during the match, scoring the equaliser that took the game to penalties in the second half of extra time, before missing the decisive spot kick.

The Gers drew first blood in the 16th minute as former Celtic man Kenny Miller kept his composure inside the penalty area and slid the ball beyond Craig Gordon, after the Hoops had failed to deal with a free kick.

The Premiership champions should have drawn level in the 39th minute when Leigh Griffiths's effort from the edge of the box came back off the far post and fell kindly for Patrick Roberts to tap in, but the youngster could only find the side-netting.

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Celtic started the second half on the front foot and draw level in the 50th minute following a series of corners, the latter of which was headed into the top corner by Danish defender Erik Sviatchenko.

The match headed into extra time with Celtic looking in control, but they were pegged back in the 96th minute by a thunderbolt from Barrie McKay, the midfielder's effort from outside the box curling into the top corner.

However, there was another dramatic twist as Rogic smashed an equaliser into the bottom corner just 30 seconds into the second half of extra time, following good work by Kieran Tierney.

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An Old Firm match had never been decided by a penalty shootout in a major competition, but that changed after 120 minutes of intense football.

The pendulum swung in Celtic's favour three kicks into the shootout when James Tavernier blazed his effort over the bar, but a subsequent miss by Callum McGregor left things all square.

Misses from Nick Clark and Scott Brown sent the shootout into sudden death, before Rogic fired over the bar with the score at 5-4 to Rangers, sending the Gers into next month's final.

Mark Warburton's side, who have already won the Scottish Championship and League Challenge Cup this season, will meet Hibernian in the final on May 21.