Cech's failure to punch the ball clear on the half-hour allowed Royals substitute Andre Bikey to give the home side the lead with his first touch.But Lampard levelled in the 47th minute and three minutes later Drogba preserved Chelsea's 100% start to the season when he curled a 20-yard effort beyond Marcus Hahnemann to keep them hot on the heels of Everton at the top of the Premier League.
Torrential rain before kick-off had left the playing surface extremely slippery but Chelsea mastered them quicker than the home side and should have taken the lead in the fifth minute.
Paulo Ferreira fed Shaun Wright-Phillips on the right flank and his cross found Drogba unmarked on the edge of the six-yard box.
But the Ivorian striker, who scored 33 goals last season, smashed his right-foot volley against an upright.
• Mourinho praises battling spirit
Reading responded by winning a succession of corners and Ivar Ingimarsson sent a header flashing just wide of Cech's left-hand post in the seventh minute.
Reading's Shane Long was booked for a foul on Ferreira in 13th minute and moments later Kalifa Cisse followed him into Mike Dean's notebook for a similar offence.
Chelsea striker Salomon Kalou thought he should have had a penalty when he went down under the challenge of Michael Duberry in the 19th minute but Dean ignored his appeals.
Two minutes later, Drogba wasted another good chance when he collected a corner at the far post only to send his effort high into the crowd.
Reading were forced to make a change in 29th minute when Duberry was injured but it turned out to be a fortuitous one for Steve Coppell's side.
Bikey replaced the former Chelsea defender and moments later scored with his first touch of the ball.
A long free-kick was headed back into the six-yard box by Long and although Cech went to punch the ball clear he was hampered by the close attention of Sidwell and Tal Ben Haim as well as Reading striker Kevin Doyle.
When the Czech Republic international completely missed the ball, Bikey ran clear to prod it home from close range in the 30th minute.
The goal gave Reading extra impetus and moments later Doyle forced Cech to save his 18-yard shot at the second attempt.
In the 34th minute, Reading should have gone two in front when Stephen Hunt's far-post cross was smashed against the post by John Oster.
It was a lucky escape for Chelsea whose situation worsened when central defender Ricardo Carvalho limped out of action with a knee injury. He was replaced by Glen Johnson.
Reading were clearly in the mood to increase their lead and Oster's fine run into the area was only let down by his wayward final ball.
Chelsea, stunned by the ferocity of Reading's attacks, finally won a corner on the stroke of half-time but Ben Haim's header was easily dealt with by Hahnemann.
Chelsea replaced Ferreira with Mikel John Obi and Sidwell with Claudio Pizarro at half-time as Jose Mourinho's side looked to get back on level terms.
The double substitution paid dividends as Chelsea equalised within two minutes of the restart.
Both Pizarro and Drogba supplied clever back headers to a long clearance and stand-in captain Lampard burst into the penalty area, controlled the ball, and beat Hahnemann from close range.
It was the perfect start for Mourinho's side and they took the lead in the 50th minute through Drogba.
The Ivorian hitman played a clever one-two with Kalou before sending a 20-yard curling effort beyond the outstretched Hahnemann for his first of the season.
The double salvo had stunned Reading who were now finding it difficult to cope with Chelsea's fluid attacking movement.
Mikel's extra physical presence in the centre of the Chelsea midfield had given Lampard some much-needed assistance and the pair were now dictating the pace of the game.
A rare Reading foray into the Chelsea half caused panic in the visiting defence, which ended with Doyle smashing the ball straight at Cech.
But it was an isolated moment for the home side and in the 68th minute Pizarro almost made it three for Chelsea when he sent a left-foot effort across the face of the goal.
Reading's woes continued when Kalifa Cisse was sent off for a foul on Pizarro on the 72nd minute and Chelsea held on comfortably to record their second successive win.
Mourinho praises battling spirit
Jose Mourinho's bravery was matched by his players as Chelsea continued their
100% start to the new campaign with a deserved 2-1 victory over Reading at the
Madejski Stadium.
Mourinho declared: 'I think the players were brave and fought a lot. They
were brave to accept some of the difficult situations. It was not easy for Shaun
Wright-Phillips to play right-back or for Glen Johnson to play as a central
defender.
'It was not easy for Tal Ben Haim after just two months at the club to find
himself leading the defence.
'But I asked them at half-time if somebody was feeling a bit weak or feeling
a bit of an injury. I wanted to make two changes and I wanted to finish with 11
men.
'They told me everybody was fit and ready to go so I made the changes. When
we were leading 2-1 there were no more changes I could make. I could have made
if more defensive but I thought our positive attacking would help us score more
goals.
'It is difficult to come to this stadium and win so I am very please with the
result and the players.
'Making the changes was a big gamble but if one day it doesn't work - like at
Newcastle in my first season - I am criticised. But I sleep good because I
tried.
'The worst thing in life is when you don't try. That is the message I give to
my kids all the time. I have to try in my job.'
Mourinho would not be drawn on whether Cech had made a genuine error or
whether he had been pushed as he rushed out to punch the ball.
His mistimed punch allowed Bikey to score with his first touch after he had
replaced injured Michael Duberry seconds earlier.
Mourinho said: 'I don't know if it was a mistake or push. But if it was a
mistake by Petr no problem, and if it was a mistake by the referee, who had a
good game, then no problem.'
Reading were further hampered by the loss of Kalifa Cisse in the second half.
He was sent off for a second bookable offence after fouling Claudio Pizarro in
the 72nd minute.
But despite the defeat, Reading boss Steve Coppell remained in an upbeat
mood.
Coppell said: 'I am disappointed but maybe I would be more critical of our
finishing in the first 45 minutes.
'When we were 1-0 up we had some really good opportunities to be more in
front. We knew they would make changes at half-time given the quality of their
players.
'We knew the changes would ask different questions of us. They played with a
lot more depth in the second half and that allowed Frank Lampard to push on for
the first goal which was a bad one from our point of view in lots of ways. But
their second goal from Drogba was great finish.
'When you go down 2-1 so quickly in the second half all the energy at
half-time evaporates. It was hard for us to get into the game and the sending
off made it very, very difficult.'
Coppell thought Pizarro made a meal of Cisse's challenge and claimed there was
a foul on John Oster prior to the incident.
Coppell added: 'There was a foul on Oster before the alleged foul by Cisse.
'By the reaction of the player you would think there had been heavy contact.
He laddered his sock so it must have been a bad injury.
'But when you've been booked in the first half then you are always treading a
dangerous line. It's an expensive lesson he's learned.'
Reading 1 - 2 Chelsea
