The cup Holders' last visit to Station Park had taken place in 2002 when a Billy Dodds hat-trick helped them on their way to a 6-0 win and an eventual Hampden cup triumph - 3-2 over Celtic.
On a bitterly cold night the Cup Holders made six changes from Parkhead with Steven Whittaker, Steven Naismith, Maurice Edu, DaMarcus Beasley, Kenny Miller and Kris Boyd replacing Kirk Broadfoot, Steve Davis, Pedro Mendes, Barry Ferguson, John Fleck and Kyle Lafferty.
The Ibrox men had struck in the opening minute of the 2002 cup-tie - but there was to be no such lightning start tonight - although Whittaker did send a left-foot shot inches wide from a Beasley cross in three minutes.
The opening goal was only delayed five minutes however - Sasa Papac coolly netting after Edu's penetrating run had ended with a pass to Miller, the ball breaking off the striker into the Bosnian's path.
There was a scare for the 4,718 spectators when the additional floodlights introduced for the benefit of television failed after quarter-of-an-hour - but play continued without interruption and the lights were soon restored.
Home goalkeeper Alistair Brown was equal to the task in seventeen minutes when he held Boyd's header from a Whittaker cross - and again from a 22-yard shot from the full-back two minutes later.
Brown again defied the Cup Holders just on the half-hour mark when he parried a Beasley rocket shot from the edge of the box after the American had been played in by Miller.
Three minutes later Allan McGregor - who must have been frozen solid with the inactivity - tangled with Andy Tod, and both players must have been thankful that Referee Eddie Smith was lenient enough to be content with a lecture to both.
Tod might even have equalised in 36 minutes when the ball broke to him following a Kevin Gordon corner - but his fifteen-yard shot was wide of the target.
Miller produced a stunning and spectacular overhead kick three minutes later from a Boyd header only to be denied by a one-handed save from Brown.
The first-half ended with the SPL side ahead by just the one goal - a situation that the travelling support were not best pleased with.
Boyd had the ball in the net five minutes after the restart from a Naismith flick only for the goal to be disallowed for offside.
Rangers were after a killer second goal - and Beasley might have got it in 52 minutes when he cut in from the right only to see his low shot held by Brown.
Sixty seconds later however it was 2-0 when Miller took full advantage of a Stephen McNally error to rifle the ball home from fifteen yards.
Lafferty replaced the ineffective Boyd in 64 minutes.
Five minutes later the 'Loons' were reduced to ten men when Elliot Smith received a straight red card for a shocking tackle on Beasley who as a consequence limped off to be replaced by Aaron.
Naismith twice came close to getting his name on the score-sheet - firstly in 78 minutes when he headed wide from a Madjid Bougherra cross, then two minutes later his shot was held by Brown following a surging run from Aaron.
Rangers had meanwhile suffered another injury blow when Lee McCulloch limped off to be replaced by Steve Davis.
Miller might have added a third in 81 minutes when his chip from a Bougherra pass was held by Brown- but to the delight of the 'Gers fans it was Aaron who did exactly that two minutes later when he netted from a Lafferty pass.
Such was the Spanish youngster's delight that he took off his jersey, receiving a yellow card for his sins.
The Third Division side had tired in the closing stages - and conceded a fourth in the last minute when a long cross to the back post by Davis found Lafferty who headed back across the face of goal to Miller who had a simple task to nod home.
Afterwards a satisfied Ally McCoist stressed:
"We were comfortable in the end. We were more direct in the second-half and scored some really good goals. Aaron gave us life and energy when he came on."
FORFAR ATHLETIC Brown; McNally, Smith; Winter (Fotheringham 73), Tod, Tulloch; Gordon (Donnachie 86), Brady (McGuigan 73), Lilley, Campbell, G. Gibson
UNUSED SUBS Kilgannon, J. Gibson
RANGERS McGregor; Whittaker, Weir, Bougherra, Papac; Naismith, Edu, McCulloch (Davis 78), Beasley (Aaron 69); Miller , Boyd (Lafferty 64)
UNUSED SUBS Dailly, Alexander
REFEREE Eddie Smith