Nani opened United's account, with John O'Shea and Carlos Tevez increasing the lead before half-time, and Cristiano Ronaldo's penalty ensured a Giles Barnes double did no lasting damage.
But the real price of a likely meeting with Tottenham will be assessed in the treatment room as Ferguson assesses injuries picked up by Rafael and Jonny Evans - part of an already depleted defence - and Nani and Anderson, who departed on a stretcher after the final whistle.
Ferguson paid a warm tribute to Nigel Clough in his programme notes and there might have been something more for the Derby boss to cheer had Martin Albrechtsen been on target with a dipping 25-yard strike.
Ben Foster, surprisingly preferred to Tomasz Kuszczak in the battle of United's stand-in keepers, was well beaten but the effort flashed narrowly wide.
It proved to be the only chance Derby would have to extend the lead in front of their 10,000-strong travelling army before the hosts took a grip of the contest.
Nani has attracted plenty of critics for a disappointing second season at Old Trafford, with some believing Zoran Tosic has been bought from Partizan Belgrade to effectively usurp the Portugal international.
But if he is not quite Cristiano Ronaldo, Nani is capable of flashes of genius, one of which he put United in front with.
Offered far too much space to run at the Derby defence after collecting Anderson's pass, Nani galloped 30 yards and then unleashed a curling shot that former United goalkeeper Roy Carroll could only push further into the corner.
With only 15 minutes on the clock, it was an ominous sign for Clough.
And his worst fears were soon realised as the kind of ridiculous mistake that got Paul Jewell the sack reared its head as Danny Welbeck slipped a pass through to O'Shea.
The Derby defence appealed for offside in unison, including Gary Teale, who had been standing half a yard behind the Irishman when Welbeck played the pass.
O'Shea may be a defender but his prowess in front of goal is well known and he calmly beat Carroll.
Tevez added a close-range third, powering home a header after Rafael had supplied the perfect inswinging cross to emphasise the hosts' superiority as they obliterated Derby's gains from a fortnight ago.
It was a completely different United team to the one that was so woeful at Pride Park when Ferguson admitted they were fortunate to be still in the tie.
Rafael was one of the men transformed. When he darted onto Ryan Giggs' perfect return pass, all the Brazilian needed was a first-time finish to convert a truly memorable move. Disappointingly, he crashed his shot into the side-netting.
Unfortunately for the Brazilian, he limped off shortly afterwards, and United's defensive problems increased when Jonny Evans also sustained an injury 18 minutes from time that left him limping badly.
Derby took Evans' lack of movement as the cue to have one final assault on the United goal and it was no surprise the Northern Ireland defender was the man to upend Green, allowing Barnes to tuck home the penalty that left United with 11 minutes to hold on.
As Ferguson had introduced James Chester for his debut by that stage and Evans was not running freely, the Red Devils decided attack was their best form of defence.
Carroll produced a fine double save to deny Ronaldo and Nani, but when he brought down Tevez on United's next attack, Ronaldo ended a domestic scoring drought stretching back to November 15 from the penalty spot.
But as Nani limped off and Anderson ended the contest hobbling badly, it was hardly an unqualified success for the home side even before another Barnes consolation.
After the match Derby manager Nigel Clough was left to reflect on what could have been as his side threatened an upset when Giles Barnes scored from the penalty spot to put his side back in it.
"If we would have got the second at home maybe things could have been different," Clough told Sky Sports."We couldn't do anything about the first goal tonight but the second was a killer really."Rob Hulse had a good chance with a header but nothing seemed to drop for us. It was good for Giles to get a couple, he's been out for a long time ."Clough admitted that his side's performance was a marked improvement on his first game in charge which ended in a 2-0 loss against QPR."It was a big improvement actually on Saturday," he added."We kept playing and plugging away and we showed a lot of character after Saturday. That's what I was looking for.""United can beat anyone on their day by four, five or six so we have a lot of positives to take from tonight."Manchester Untied manager Alex Ferguson refused to let his side's injury problems take the shine off his young side's victory.Youngsters Danny Welbeck, Darron Gibson and Rafael all helped United on their way to a 4-2 win and he chose to sing their praises following the win, rather than concentrate on the injuries picked up by three of his key players tonight."We have a few injuries tonight so it has been a bad night in that respect but we are in the final and we should be celebrating that," Ferguson said."Finals are always hard to get in to and the young lads have done fantastically well to get there. It was a great performance and they (the youngsters) will all be playing in the final."The important thing is to find out what their temperament is and they have all proved that tonight. Playing in big occasions in front of 75,000 is difficult and I'm proud of themJonny Evans, Rafael and Anderson all picked up injuries during the match."Anderson's going to have to go for an X-ray," Ferguson added. "There's some damage. We're not exactly sure what but we'll see what happens"Evans has had a recurrence of ankle injury that he has been holding for a few weeks, but hopefully he'll be back next week."Rafael has a hamstring injury and he'll be out for a few weeks."
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