Chelsea scored twice in three minutes to maintain their 100% record as goalkeeper Petr Cech endured an uncomfortable return to Reading.
Drogba scored with a sumptuous shot for his first goal of the season
Cech, who fractured his skull last season in the game at Reading, made an awful hash of a punch allowing Andre Bikey to put the home side ahead.
But Frank Lampard's run and shot early in the second half and Didier Drogba's curling effort put Chelsea 2-1 up.
Reading went down to 10 men when debutant Kalifa Cisse was red-carded.
On Sunday Steve Coppell had tactically outmanoeuvred Sir Alex Ferguson at Old Trafford and the first-half saw the Reading manager outwit Jose Mourinho.
Reading produced a high-octane pressing game that allowed Chelsea no time to settle and Coppell's side were well worth their first-half lead, albeit with a helping hand from Cech.
This was the first time Chelsea's Czech Republic keeper had been back to the Madejski and his failure to punch the ball clear from Ivar Ingimarsson's header proved costly.
While Cech and a couple of Chelsea defenders were left in a heap, Bikey had the simplest of tasks in putting the ball in the net.
It was the first touch of the ball for Reading's Cameroonian defender, who seconds before had come on for the injured Michael Duberry.
Soon afterwards John Oster was unfortunate not to extend Reading's lead when his volley cannoned back off the post.
If Coppell emerged victorious from the first-half tactical battle, Mourinho showed he is no slouch when it comes to strategical thinking.
Never one to dally with substitutions the Chelsea manager used his two final substitutes - John Obi Mikel and Claudio Pizarro - at the start of the second half.
Steve Sidwell was one of the players withdrawn as the former Reading midfielder made an unhappy return to his former club.
Mourinho's reshuffle brought immediate results - within two minutes of the restart Lampard's marauding run into the Reading box gave him the space to slip the ball past Marcus Hahnemann.
Three minutes later Reading's American was beaten again - this time from long range - as he was left clutching thin air by Drogba's superb shot.
Those two goals knocked the wind out of Reading, who struggled to hurt Chelsea in the second half in the way they had done in the opening period.
Reading's hopes of salvaging anything from the game further receded when Cisse was sent off after collecting his second yellow card on 72 minutes.
Not that Chelsea did not emerge from this win without casualities, with Ricardo Carvalho going off injured in the opening half.
Reading manager Steve Coppell:
"Our downfall was not finishing off the chances we'd created.
"At the interval we were a bit disappointed not to be further ahead.
"Then they they made changes and that gave the game a different complexion.
"We fell asleep for five minutes and gave away a poor goal defensively and Didier Drogba scored a very good one."
Chelsea manager Jose Mourinho:
"We made changes and the players were brave enough to accept the risk of the way we played.
"The reaction was amazing. I just feel sorry we didn't score a third.
"As on Sunday we had to suffer, but six points in two games is a good start for us. This is a very good place to win as Reading are a very difficult side."
Reading: Hahnemann, Murty, Ingimarsson, Duberry (Bikey 29), Shorey, Oster (Ki-Hyeon 79), Harper, Cisse, Hunt, Doyle, Long (Gunnarsson 74).
Subs Not Used: Federici, De la Cruz.
Sent Off: Cisse (72).
Booked: Long, Cisse, Hunt, Ingimarsson.
Goals: Bikey 30.
Chelsea: Cech, Ferreira (Pizarro 46), Ben Haim, Carvalho (Johnson 31), Ashley Cole, Wright-Phillips, Sidwell (Obi 46), Lampard, Malouda, Drogba, Kalou.
Subs Not Used: Cudicini, Joe Cole.
Booked: Carvalho, Sidwell, Wright-Phillips, Ashley Cole, Obi.
Goals: Lampard 47, Drogba 50.
Ref: Mike Dean (Wirral).