Oscar gave the west London side a fourth-minute lead at Carrow Road when he expertly curled home Demba Ba’s cut-back with the outside of his boot.
But the battling Canaries refused to give in and drew level in the 68th minute when Anthony Pilkington headed in.
However, despite an onslaught of Norwich pressure, substitute Hazard poked a finish past City goalkeeper John Ruddy five minutes from time to make it 2-1.
And the Belgian’s fellow substitute Willian powered in a delightful third moments later as the Brazilian netted his first Blues goal in style.
“When I make a change, the change is always fantastic and the players make it fantastic or make it rubbish – it’s up to them,” said Mourinho.
“I’m happy for Willian because he is starting with us, he is not 100 per cent. He was injured in the week and the kid made himself available to try to help, and when he came on he gave us a push.”
Chelsea moved up to third place in the table after securing their first Premier League away win of the season.
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