Celtic hammered hapless 10-man Rangers 4-0 at Hampden Park to book a William Hill Scottish Cup final date with Motherwell next month.
Tom Rogic swept the Hoops into the lead in the 22nd minute and fellow midfielder Callum McGregor made it 2-0 with a drive in the 38th minute of a startlingly one-sided encounter.
Five minutes after the break Gers defender Ross McCrorie was given a straight red card by referee Bobby Madden for denying Moussa Dembele an obvious goalscoring opportunity, and from the resultant penalty the French striker scored 'Panenka' style for his seventh goal in nine Old Firm games.
The Ibrox side rallied in desperation but midfielder Olivier Ntcham scored a fourth from the spot in the 78th minute with Graeme Murty's side fortunate to finish with no further damage.
If Murty harboured any prospects of keeping the job next season then they were surely heavily damaged by a Hoops side who have now gone 10 games unbeaten against Rangers under Celtic boss Brendan Rodgers.
Celtic beat Motherwell in the Betfred Cup final in November and will meet the Fir Park side again in the showpiece finale on May 19.
They will be strong favourites to win a historic second successive treble, their seventh Ladbrokes Premiership title in a row a mere formality.
The Parkhead side made their intentions known right from the kick-off.
In the fifth minute of a typically frenetic start to this Glasgow derby, Dembele volleyed a Ntcham cross off the post with the Light Blues defence getting the ball to safety.
The Hoops, sharper in possession and quicker in thought, dominated possession.
A couple of Celtic corners flashed across Rangers' six-yard box before Rogic took a pass from James Forrest and turned back on to his right foot, leaving McCrorie for dead, and then from 14 yards guided the ball almost casually past Rangers goalkeeper Wes Foderingham
Moments later, the Australia international had another chance but this time his weak effort was caught by Foderingham.
Celtic were simply playing at a higher tempo and in the 32nd minute Ntcham fired just wide from the edge of the box.
A timid-looking Rangers could not get hold of the ball for any length of time.
However, it was a horror mistake by Rangers defender Russell Martin which handed Celtic their second. His attempted clearance from Kieran Tierney's cross went straight to McGregor who gleefully and quickly curled the ball past Foderingham.
Midfielder Andy Halliday was immediately replaced by Josh Windass and he made his unhappiness clear as he took his seat in the technical area.
Any thoughts of a comeback ended early in the second half when McCrorie pulled back Dembele as he raced through on goal and after he was given his marching orders, Dembele dinked his spot kick down the middle with Foderingham diving to his left.
Bruno Alves was put on for Daniel Candeias and the veteran Portuguese defender forced a good save from Craig Gordon with a header, seconds after the Hoops keeper had made a similarly impressive save from Alfredo Morelos.
The Colombian striker then missed a great chance, hitting the ball straight at Gordon, after Celtic defender Mikael Lustig's sliced clearance had come off his own crossbar.
Forrest bent a shot wide of the target before Rangers substitute Jason Holt, on for Graham Dorrans, conceded a penalty for a foul on Patrick Roberts, replacement for Forrest, and Ntcham despatched the spot-kick into the corner of the net.