With the win, Celtic's bid for a historic back-to-back treble continues - with Motherwell standing in their way after they beat Aberdeen in the other semi-final yesterday.
The Hoops thumped Rangers at Hampden Park and were inspired by their Australian midfielder, who opened the scoring with a crafty piece of skill in the 22nd minute.
Celtic were the better team from start to finish, and it did not help Rangers' cause when Ross McCrorie was dismissed in the opening minutes of the second half.
Celtic's social media had been of interest before the game when the club's official Twitter account referred to "the Ibrox side" rather than Rangers.
Martin's attempted clearance from Kieran Tierney's cross went straight to McGregor, who quickly curled the ball past Foderingham.
It resulted in the sending-off of McCrorie, and Celtic striker Dembele subsequently successfully converted the spot kick.
Forrest bent a shot wide of the target before Rangers substitute Jason Holt conceded a penalty for a foul on Patrick Roberts in the 78th minute.
Moussa Dembele hit the post inside five minutes from Olivier Ntcham's wonderfully placed cross into the box which set the tone for the afternoon.
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