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.
Lampard's pass from inside his own half was brought down by Ba inside the City box and the striker, with Turner backing off, laid the ball off for
Oscar to hit it first time with the outside of his right boot into the bottom corner.
It was a fine goal, but Norwich made it all too easy for the visitors.
Mata was then granted space to pick his pass after drifting in field and found Ba, whose effort was well saved by Ruddy.
Ruddy lost an aerial duel with Ba, who turned and shot only for Bassong to block.
Norwich enjoyed some openings down Chelsea's right, with Martin Olsson and Leroy Fer's pace troublesome, but it was from down their own right flank that they nearly equalised when Ricky van Wolfswinkel's cross was prodded wide by Jonny Howson.
Ruddy recovered to concede a corner after Ba won another aerial challenge with Turner and the goalkeeper before Norwich pressed again without testing Petr Cech.
David Luiz had Ruddy back-pedalling with a shot from a yard inside Norwich's half as the ball landed on the roof of the net.
Cech was called into action for the first time when Bassong shot straight at him from a corner as the half came to a close which Chelsea dominated without adding to Oscar's early effort.
The visitors so nearly made a flying start to the second half as Schurrle and Ramires combined down the left and the latter crossed for Ba.
With just Ruddy to beat, Ba failed to cleanly connect and the ball went wide.
Ramires was soon in action at the other end, dispossessing Pilkington, who went down, but Swarbrick was unmoved as the hosts appealed for a penalty.
Terry got in ahead of Van Wolfswinkel and then blocked from Pilkington as Norwich threatened again before equalising.
Martin Olsson's deep cross from the left created havoc and found Van Wolfswinkel.
The Holland striker met the ball at the back post and centred for Pilkington, who got the wrong side of Luiz and headed past Cech, who should have done better.
Cole's departure forced a change in tactics for Chelsea, who threw players forward.
Branislav Ivanovic, popping up on the left, forced a save from Ruddy and then Eden Hazard, Cole's replacement, fired narrowly wide.
Norwich had chances, too. Nathan Redmond, on for Snodgrass, had an effort saved by Cech before Olsson lost his balance in the act of shooting.
Redmond was lively and won a corner with five minutes remaining - but it led to a goal for Chelsea.
The Blues broke and Alex Tettey was unable to deal with Oscar's cross-field pass, allowing Hazard to pounce.
The Belgium forward's shot squirmed under Ruddy, who could only scramble forlornly as the ball went over the line.
A minute later, Ruddy could do nothing as Willian put a gloss on proceedings by curling into the top corner.