It was Ballack who nodded Chelsea in front just before halftime.
The Germany captain was left unmarked at the far post to head home Drogba's cross in the 45th minute.
United got themselves back into the game after the break thanks to a monumental blunder by Carvalho.
Drogba then clashed with Ballack over the taking of a free-kick. Ballack stormed off, leaving Drogba to take it and Edwin van der Sar pulled off a magnificent save. The row continued during treatment to John Obi Mikel, with Drogba firing verbals at both Ballack and Blues coach Steve Clarke.
Then in the final five minutes, Chelsea were awarded a penalty after Michael Carrick was penalised for handling in the area. Ballack stepped up and converted coolly - and among the first to congratulate him was Drogba.
But the action was still not over as first substitute Cristiano Ronaldo saw his left-foot drive cleared off the line by Ashley Cole before Blues striker Andriy Shevchenko did the same to block Darren Fletcher's injury-time header.
Chelsea's victory brings them level on 81 points with leaders United, who remain top on goal difference with now two games to play.