Barcelona had scored in every home game this season and were last held at home by Manchester United at the same stage of last year's competition.
Strikers Lionel Messi, Thierry Henry and Samuel Eto'o had scored 90 goals between them in all competitions this season but Chelsea's terrific defensive discipline kept them at bay.
Cech made fantastic saves from Henry, Daniel Alves, Aleksandr Hleb, and Eto'o to give Guus Hiddink's men a great chance to reach their second successive Champions League final.
Hiddink hailed captain John Terry as "inspirational" after the game and while Cech agreed, the Czech Republic keeper was also full of praise for the rest of the side - particularly Jose Bosingwa.
The Portugal international was given the task of marking Messi out of the game and did so in style.
"I think the biggest compliment should go to Jose because I think it was the second time in his life that he played at left back and it was against Messi," he said.
"But you couldn't see Messi on the pitch today. John was also fantastic and I have to say so were all the other guys because it is not easy to come here and deal with all their attacking threat.
"But John was the leader of the back four and was brilliant. It is the first time we have got a clean sheet here but it is also the first time we haven't scored.
"The tie is still open but I think we can reproduce the same defensive work at home and we can always score goals at Stamford Bridge.
"Of course they have the best attack in the world, so it still stays 50-50.
"We just had to stay organised and everyone had to put in great effort for the individual and tactical work.
"As a team we had a great effort and we were rewarded with a clean sheet. But it was a pity that we had two good chances that could have been a goal. The goal would have been better but 0-0 is still a positive result.
"We wanted to stop them playing and then put them under pressure with our possession, which in the first half we didn't really do."
Coach Hiddink was quick to praise Terry and Cech for their all-important contributions on a great night for the Blues.
"John was inspiring, an example for the rest of the team," said Hiddink.
"You have to play courageously and play with a lot of intelligence against Barcelona, you cannot just play a tough game.
"This team has a lot of courage and a lot of blood, mentally it was great performance.
"Petr did a good job defensively, he intervened in one or two situations and he saved the game for us.
"If you look at the recent history of Barca, you will see it is a long time since they last failed to score in a home game.
"That's quite an achievement against a beautiful team who play beautiful football."