Drogba, who re-joined the club from Galatasaray this summer, took a knock just half an hour into the Blues' final European friendly and was replaced by Oscar.
Former West Brom forward Zoltan Gera put the hosts ahead just before half-time before Ramires levelled with a wonder-strike from distance.
And then half-time substitute Fabregas, signed from Barcelona in June, won the game on 81 minutes with a classy solo goal.
Youngsters Kurt Zouma and Andreas Christensen partnered at centre-back in a first eleven that also included new left-back from Atletico Madrid Filipe Luis.
Andre Schurrle and Drogba both went close for Jose Mourinho's side before the Ivorian was forced off after Gera's opener.
Schurrle's brilliant free-kick that missed by a few inches was Chelsea's best chance of the first half, but they remained behind and so Mourinho brought on Branislav Ivanovic, Gary Cahill, Mohamed Salah, Fabregas and Diego Costa at the break.
Ramires controlled with one touch and fired viciously into the top corner to bring Chelsea level on 51 minutes before Cahill threatened with a free header and Oscar also went close
But Fabregas – who had an outstanding second half - produced a moment of pure class, breaking through midfield and firing in, with shades of Frank Lampard, to win the game late on.