Second-half goals from Eden Hazard and Ramires had pulled the visitors level after Javier Hernandez and Rooney struck early.
It seemed certain Juan Mata would complete a memorable comeback when he stepped inside Jonny Evans in the final minute.
But David De Gea, so often the target of criticism, stuck out a leg to keep Mata out and United in the tournament.
The replay will not suit Ferguson, still less so Rafael Benitez given it could potentially force Chelsea into four games in a week or trigger the postponement of a Premier League fixture.
However, both have reason to be thankful, United because their collapse from a position of such immense promise could so easily have been total, Chelsea as at half-time it seemed Benitez was being given another hefty shove towards the Stamford Bridge exit door.
It had all been about Rooney before kick-off, given the intense speculation that followed his omission from the United side that faced Real Madrid on Tuesday.
Yet from the moment he was captured bouncing off the United team bus with a wide smile of greeting for the security staff in attendance, it seemed certain this would be a day of redemption.
Rooney's name was chanted by the United faithful, not in criticism of Ferguson, but in confirmation of the striker being one of them, part of a United family so carefully pieced together by their manager, who until Nani's dismissal in midweek truly believed another Treble was on.
Hernandez, someone with just as great a claim on a starting berth and whom did not appear for a single minute against a team held in so much affection in his native Mexico, had already struck in quite spectacular fashion before Rooney found the net.
Lining up a free-kick wide on the United right, level with the penalty area, Rooney aimed for the far corner.
David Luiz and Jonny Evans both jumped but missed it and by the time Chelsea goalkeeper Petr Cech could react it was too late. The ball flew into the corner and Rooney had his goal.
e did not really mean it but he took the acclaim anyway, raising his arms and turning slightly to acknowledge those in rapturous celebration.
Rooney nearly got a second in first-half stoppage time, as he deliberately sent another free-kick from a similar position on the other side of the pitch fizzing on to the roof of the net.
United's only other opportunity of that opening period also involved Rooney, but it was far more notable for a ridiculous attempted clearance from Luiz after Cech had saved Rooney's shot, which forced his goalkeeper into another reaction save.
Amid all this, Chelsea had done quite well.
Frank Lampard came close on a couple of occasions, Mata teased the United defence and rolled an inspired backheel into the path of Victor Moses, only for the former Wigan man to screw his shot so badly wide it actually hit the corner flag, prompting the rather cruel taunt of "Are you Torres in disguise?" from the home support.
The vitriol from the away contingent to their own 'interim' boss was even worse when Benitez took Lampard off as part of a double change nine minutes after the re-start.
But Benitez is not quite the no-nothing Chelsea's disgruntled supporters think and his tactical switch worked a treat as one of the men introduced, Hazard, injected fresh hope into the Blues by curling a superb effort into the far corner beyond De Gea.
The impetus it gave Chelsea was marked, and when Rooney lost possession deep in the visitors' half, United were caught out with a classic counter-attack that ended with Ramires expertly drilling home.
It was the second time this season the Brazilian had completed a Chelsea comeback from two goals down against United.
On the first occasion, at Stamford Bridge in October, Chelsea then had two men sent off and were beaten by Hernandez.
This time they managed to keep everyone on the pitch and they would have been the ones to claim victory had it not been for De Gea.