The Red Devils were always in pole position having won the quarter-final first leg at Stamford Bridge 1-0 - and took complete control of the tie on 43 minutes when Javier Hernandez smashed home from close range following a fine cross from veteran Ryan Giggs.
Chelsea had started with Fernando Torres up front, but he was hauled off at half-time and replaced by Didier Drogba.
The visitors had Ramires, John Terry and Florent Malouda on yellow cards in the second half, and Ramires was sent for an early bath after clumsily fouling Nani to see yellow for a second time.
Drogba brought the tie to life on 77 minutes, though, when he latched onto a cracking Michael Essien pass and slotted past Edwin van der Sar.
United were ahead again in the same minute, however, as Giggs' sublime lofted pass found Park Ji-Sung, who controlled and despatched a clinical left-footed strike into the net.
Sir Alex Ferguson's troops now face Schalke or Inter Milan in the last four on April 11.
Carlo Ancelotti's mighty gamble on £50million man Torres backfired to place a massive question mark over his future as Blues boss.
As Ferguson has noted, Roman Abramovich is obsessed by winning this competition.
As the Russian was in the directors' box, looking down as United emerged triumphant, it can only be concluded he is not a happy man.
And with Ancelotti insisting he is under no pressure to play Torres, the only conclusion to be reached is that he will carry the can for what was so obviously a gross selection error.
While Torres has now failed to score in 11 Chelsea games, Drogba continues to look a threat.
He was the man who briefly threatened to derail United after Ramires was sent off.
It was a false dawn. Chelsea are staring down the barrel of a trophyless season and Ancelotti will be in the firing line if Abramovich decides to pull the trigger.
No-one could accuse the Italian of shirking the big decision and it was true that Chelsea's first-half performance was vastly superior to their efforts at Stamford Bridge six days ago.
Not that Torres could claim much of the credit.
He did glance an early header wide after climbing above Rio Ferdinand, who was hampered by an injury not serious enough to force him off but that undoubtedly restricted his movement.
After that, the game generally passed Torres by at a ripping pace.
Nicolas Anelka was narrowly wide with a half-volley that came about as a direct result of a Torres mis-hit and when the Frenchman intercepted a poor clearance by Nemanja Vidic, it looked like he would get a clear sight of goal until van der Sar robbed him with a perfectly executed slide tackle.
With Ramires the driving force in midfield, it seemed only a matter of time before Chelsea were back on level terms.
They certainly should have been when Malouda raced into the box, then teed up Frank Lampard with a perfectly weighted square ball.
For once, the midfielder's finish was not good enough, containing insufficient power to beat van der Sar.
But with Vidic and Ferdinand standing firm, United survived, allowing Wayne Rooney to cause mayhem at the other end.
Operating in a deep role just behind Hernandez, more than anyone, Rooney dictated the pace of the Red Devils' play.
It was the England striker, who will be suspended on Saturday when United tackle City in a Manchester derby FA Cup semi-final, who fizzed over the cross from which Hernandez thought he had put the hosts in front, only to be flagged offside.
The call was tight, equally as debatable as the one that followed in the final minute of the half as United took the lead.
Much has been made of how good this present Ferguson team actually is.
So often, it is derided for lacking stardust.
But what improvement do they gain from Giggs' experience.
When Nani's free-kick ended up being shunted back to the right flank from which it had been delivered, John O'Shea set his 37-year-old team-mate scampering into the box with an inspired reverse pass.
This is where Giggs' status in the game came in.
Rather than rushing his cross and wasting the opportunity, he took his time, looked up and delivered the ball low to the far post, where Hernandez arrived at exactly the right moment to slide it into the roof of the Chelsea net.
As his heavy punt on Torres had failed, Ancelotti rolled the dice once more at half-time, withdrawing his shot-shy striker and introducing Drogba.
The Ivorian almost levelled within a minute of the restart, just failing to find the target with a near-post flick.
A man on a mission and no mistake, Drogba whipped round Ferdinand and lashed a low 20-yard drive narrowly wide.
And, after Ramires had been sent off rather harshly for a soft foul on Nani, it was Drogba who refused to let Chelsea surrender, drilling through van der Sar's legs to breathe new hope into the visitors' challenge.
Unfortunately for the striker, as quickly as it arrived, it was snuffed out as Giggs chipped a glorious pass to Park, who fired gleefully into the bottom corner to send United into the last four, where they will almost certainly meet German challengers Schalke.