Oscar was the first of the three Chelsea midfielders to find the net at Carrow Road in the 4th minute.
After Anthony Pilkington headed Norwich level in the 68th, Chelsea manager Jose Mourinho brought on Hazard and Willian off the bench.
Chelsea’s lead was restored in the 85th after Norwich conceded possession from its corner and the visitors launched a blistering counterattack. After Alex Tetty failed to clear the ball, Hazard took advantage and unleashed a shot that squirmed under goalkeeper John Ruddy.
Willian was on target in the 86th on his Premier League debut with a curling strike into the top corner.
The victory keeps Chelsea in the top four with 14 points from seven games.
Chelsea might have had a penalty in the opening minutes of the game, but referee Neil Swarbrick raised no objections when Ba went down softly between Sebastien Bassong and Michael Turner.
It didn’t matter as Chelsea soon led through Oscar, who began in the play-maker role behind Demba Ba, with Juan Mata on the right.
Frank Lampard’s pass from inside his own half was brought down by Ba inside the Norwich 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 inside and found Ba, whose effort was well saved by Ruddy.
The Norwich goalkeeper 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 equalized 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 with Chelsea dominating without adding to Oscar’s early effort.
The visitors so nearly made a flying start to the second half as Andre 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.
Chelsea captain John Terry got in ahead of Van Wolfswinkel and then blocked from Pilkington as Norwich threatened again before equalizing.
Martin Olsson’s deep cross from the left created havoc and found Van Wolfswinkel. The Netherlands striker met the ball at the back post and centred for Pilkington, who got on the wrong side of Luiz and headed past Cech.
Ashley Cole’s departure through an apparent injury forced a change in tactics for Chelsea, who threw players forward.
Right back 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 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 with his first Chelsea goal.