Jose Mourinho's men made the 120-mile journey to Carrow Road by plane on Saturday and made a flying start when Oscar gave them a fourth-minute lead after Demba Ba's lay-off from Frank Lampard's lofted pass.
Victory from then seemed a formality for Chelsea but it appeared anything but until a late rally.
Ba might have netted early in the second half following a cross from Ramires, who was relieved not to concede a penalty when challenging Anthony Pilkington in the box.
Norwich levelled when Pilkington headed in from close range and had further opportunities, but Hazard finished off a ruthless counter attack and Willian curled in his first Chelsea goal to complete the win.
There were moments of alarm for England boss Roy Hodgson ahead of the World Cup qualifiers with Montenegro and Poland.
Ruddy, who had an opportunity to show he should be England's number one ahead of Joe Hart, should have done better in two aerial duels in the Norfolk sunshine with Ba and allowed Hazard's weak shot to beat him, while Chelsea left-back Ashley Cole departed 15 minutes from time clutching his ribcage.
Preferred to Samuel Eto'o in place of the injured and suspended Fernando Torres, Ba quickly got the better of his marker, Sebastien Bassong, who was the solitary Norwich change following the win at Stoke.
Chelsea might have had a penalty in the opening skirmishes, but referee Neil Swarbrick merely shook his head when Ba went down softly between Bassong and Michael Turner.
It mattered not as Chelsea soon took the lead through Oscar, who began in the play-maker role behind Ba, with Juan Mata on the right.
Source: PA
Source: PA