The bitter rivalry between the two clubs which have dominated Scottish football for decades is well chronicled, but Celtic's superiority as Leigh Griffiths and Kris Commons found the target took the heat out of the fixture.
It was the 400th competitive meeting, but first since April 2012, shortly before cash-strapped Rangers was liquidated and forced to re-form as a new entity in the bottom flight of the Scottish leagues.
The 2-0 win for Celtic reflected the current status of the two clubs, one topping the Scottish Premiership, the other struggling to catch Hearts in the battle for the automatic promotion spot from the second flight.
Rangers had hoped for redemption in the cup competition, but it is Celtic who will face Dundee United in the final on March 15.
Griffiths headed home the opener on 10 minutes and Commons blasted home the second just after the half hour mark.
Celtic was content to soak up sporadic Rangers pressure in the second half, with keeper Craig Gordon barely tested. It left manager Ronny Dalia satisfied with his team's efforts.
"I think 2-0 was a fair result," he said.
"In the first half we had four chances and we scored two which was okay. The second half we didn't have many but they didn't have a shot on target either."
Rangers -- without a permanent manager since the departure of Ally McCoist -- and still beset by boardroom wrangles -- will now be left to focus on its bid to win promotion back to the Scottish Premiership.
If it succeeds the Old Firm matches will again become regular fixtures -- a welcome boost to the finances of both clubs -- as they are played to capacity audiences with extra television revenues. Sunday's game was beamed live to 54 countries.
Meanwhile, in the English Premier League, Arsenal continued its recent charge with a 5-0 rout of struggling Aston Villa, without a goal in the last six league games.
The match at the Emirates was entirely one-sided and the Gunners took the lead on eight minutes when Olivier Giroud scored after an assist from Mesut Ozil.
German international Ozil added the second with the impressive Theo Walcott, watched by England manager Roy Hodgson, grabbing the third.
Santi Cazorla scored the fourth from the penalty spot with Hector Bellerin's 30-yard effort completing a fine afternoon for Arsene Wenger's men.
Arsenal has now taken 19 points from a possible 24 and risen to fifth, leapfrogging north London neighbor Tottenham Hotspur.
Fourth-placed Southampton later suffered a shock 1-0 home defeat to Swansea, ending with 10 men after Ryan Bertrand was sent off in the second half.
Jonjo Shelvey scored the Swansea goal after 83 minutes of a tight encounter.
Barcelona's title hopes in Spain stayed on track but the Catalan giants had to twice come from behind to beat Villarreal 3-2 in the Nou Camp.
Denis Cheryshev put the visitors ahead after half an hour, only for Neymar to level just before the interval.
Luciano Vietto restored the Villarreal lead on 51 minutes but it was shortlived as Rafinha leveled two minutes later.
Lionel Messi had been involved in that goal and he put Barcelona into the lead for the first time with a fine strike after an assist by Luis Suarez.
The win lifts Barca to just one point behind leaders Real Madrid, but having played a game more.