Oscar fired the Blues into a fourth-minute lead at Carrow Road when he expertly curled home Demba Ba’s cut-back.
But the Canaries refused to give in and conjured an equaliser in the 68th minute when Anthony Pilkington headed in.
However, despite an onslaught of Norwich pressure, Eden Hazard poked a finish past City goalkeeper John Ruddy five minutes from time, before fellow substitute Willian powered in a delightful third moments later.
“I thought that in the first half we had a better control of the game and we could have scored more goals than only one,” Cech told Sky Sports.
“I think that was the main difference because in the second half they got back into the game.
“They are a Premier League side playing at home and full of confidence in the second half because it was only 1-0 and they got the equaliser.
“It became much more difficult for us but the reaction was great because from the moment the equaliser went in we went up a gear and scored two fantastic goals.
“They didn’t take their chances and we punished them for that.
“We have to work hard as well and I think that there were moments in the game that everybody worked hard, no matter how talented you are. We have to stick together.”
Cech was also pleased to help Chelsea record their first Premier League away win of the season as they moved up to third in the table.
“It’s always good to have a positive start and then get better,” he continued.
“We hope to get better every game and today was an important win for us, especially after we conceded and equaliser quite late in the second half.”
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