Sir Alex Ferguson and his team will feel hard done by as Drogba was clearly offside as he collected Salomon Kalou's pass and drove home 12 minutes from time.
Related ArticlesMan Utd v Chelsea: as it happenedManchester United v Chelsea: match centreMan United v ChelseaPremier League tablePremier League fixturesTelegraph player raterThe significance of the error only became clear once Federico Macheda had pulled a goal back for the hosts to set up a pulsating finish.
But Ferguson would be aware that the first hour had been completely one-sided in Chelsea's favour and that the visitors should have had a greater advantage than the one goal Joe Cole provided in the first half.
Without Wayne Rooney, there was no real bite in United's attack. And although the 34-goal striker is only out for a fortnight, by the time he returns his side's dreams of glory might be over, considering Chelsea now have a two-point advantage and a superior goal difference.
Since his recovery from a long-term knee injury, Cole has struggled to get back into the swing of things.
Fabio Capello claimed he was not the same player when he left the midfielder out of his England squad to face Egypt last month, raising extreme doubt over Cole's chances of making the World Cup.
Cole's admission that contract talks had broken down was a statement in itself, given it is hard to imagine Carlo Ancelotti allowing a pivotal player to find himself in such a position so close to him being allowed to leave on a free transfer.
Old Trafford has been mentioned as a potential destination should Cole leave Stamford Bridge this summer, so it was an opportunity to impress Sir Alex Ferguson, not that the United chief would have found the 18th-minute opener even vaguely admirable.
Having put his side's obvious failings in possession down to a one-off in Munich last week, Ferguson must have been worried to see the same fault reappearing quite so often, quite so soon.
There is no doubt the ankle injury Rooney suffered in Germany had a negative effect on United.
But the fault lay much deeper, their play too ponderous to have any impact.
All across the midfield, United were wasteful in possession. And with Florent Malouda giving Gary Neville a right old runaround, Chelsea took complete command.
The disappointment for Ancelotti must have been that his team did not make the most of their possession.
Edwin van der Sar denied Cole on one occasion and Nicolas Anelka had a couple of shots blocked but clear-cut chances were rare.
Even Chelsea's opening goal was not a golden opportunity in that sense.
Malouda was invited to run into the home box and although Darren Fletcher eventually reacted, the Chelsea midfielder had the strength to hold him off and cut the ball back to the near post, where Cole got in front of Patrice Evra and found the net with a neat back flick.
It took United a long time to respond. And when the rally eventually came, it took the form of a couple of debatable penalty appeals and referee Mike Dean was not impressed either when Yury Zhirkov chopped down Park Ji-sung and Dimitar Berbatov fell under Frank Lampard's challenge.
Had Paulo Ferreira shown more conviction when he raced to meet Cole's excellent through-ball at the start of the second half, the contest would have been over.
Instead, the full-back failed to find either the far corner, or Anelka, and United, who at least speeded up a little bit, remained alive.
The escape certainly seemed to galvanise the hosts, who for the first time made Chelsea's defence creak.
Berbatov, the man of whom so much was expected in Rooney's absence, was just off target with a couple of headers and, off balance, Park was unable to keep his shot on target after a forceful Fletcher run had carved Chelsea open.
The introduction of Drogba midway through the second half emphasised the Blues' strength in depth compared to their hosts, who were forced to rely on the talents of teenager Macheda when Ferguson needed to reinvigorate his side.
Predictably, Drogba had an immediate impact, even if he was offside as he collected Kalou's pass before drilling his shot past Van der Sar.
Down, and almost out, United responded instantly as Cech pushed Nani's cross onto the on-rushing Macheda.
The ball bounced slowly into the Chelsea goal to set up a dramatic ending.
But the Blues were worthy winners at the end. Behind glass, in the executive box where he watched from, Rooney could only wonder what might have been.