Cech, playing his first game back at the stadium since fracturing his skull in the same fixture last season, mistimed his punch and allowed Reading substitute Andre Bikey to score with his first touch.
But Mourinho the brave replaced former Reading favourite Steve Sidwell with Mikel John Obi and right-back Paulo Ferreira with striker Claudio Pizarro at half-time.
It meant asking winger Shaun Wright-Phillips to play at right-back and Glen Johnson to play as a central defender after Ricardo Carvalho was forced out of the game with a knee injury in the opening half.
But the changes worked like magic and Mourinho emerged with another glowing testimony to his managerial reputation even though he knew he was taking another massive risk.
One more injury in the second half would have brought fierce criticism of his tactics but, unlike an FA Cup tie at Newcastle three seasons ago, his luck held this time.
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."