Dunfermline veteran Craig Brewster was the hero for the Pars with an impressive display and a goal that helped them reach the final where they will meet Celtic.
And at least they can look forward to an occasion worthy of the competition after the farcical decision to stage this supposedly prestigious semi-final replay here. Aberdeen's 21,000 capacity stadium was little more than a quarter full after the SFA rejected representation from both clubs to move the tie to the more compact and accessible McDiarmid Park in Perth.
That made it the lowest attendance at any Scottish Cup semi-final in history, easily beating the previous record set by Kilmarnock and Dundee United at Easter Road in 1997.
Caley went ahead when Paul Ritchie showed the guile that has marked him out as the most effective striker in his division by controlling a pass from David Bingham, then scoring his 21st goal of the season. Had both Bingham and Stevie Hislop possessed the same sort of composure either side of that seventh-minute goal then the tie would have been settled quickly, but they headed wide of the target from within the six yard box. Dunfermline recovered from a nervous start to produce the fine football that has troubled every side, including Celtic, at various stages this season.
The inspiration for that has often been Brewster, who scored the winning goal in the 1994 Scottish Cup for Dundee United against Rangers, and the veteran forward was crucial again. It was his intelligence in dropping deep that created the space for Lee Bullen to intrude on the left side and Brewster's delicious diagonal pass that picked out the over-lapping fullback. The near-post cross was flicked in at the front junction of the six yard area by the Darren Young in the 25th minute.
Brewster scored in the 63rd minute when, from the tightest of angles, he beat the keeper off the far post. Barry Nicholson put the tie beyond Caley's reach with a third goal 12 minutes from the end after a brilliant solo effort. Bingham got a last-minute goal from the penalty spot.