CITY lost 2-1 to Chelsea despite a spirited second half performance in an action-packed game at Carrow Road.
The Canaries got off to the worst start possible when Kenedy scored after just 39 seconds, the fastest goal of the Premier League season.
Diego Costa then doubled Chelsea's lead in first half stoppage time, although replays showed the striker to be offside when he received Bertrand Traore's pass.
City were on top for large swathes of the second half and got a deserved goal through Nathan Redmond, who blasted home from Wes Hoolahan's pass - but in the end it wasn't to be as their poor run of results continued.
Alex Neil made one change from the late 1-0 defeat to Leicester City on Saturday as Hoolahan returned to the starting eleven.
Dropping out was Steven Naismith, who wasn't involved in the matchday squad. Also still absent from the 18 was Sebastien Bassong, while Patrick Bamford was ineligible against his parent club.
Chelsea made four alterations from their 2-1 victory at Southampton, with Oscar and Nemanja Matic the notable additions to Guus Hiddink's team. Traore also made his first start for the Blues.
City would have hoped for a fast start but they got the opposite, allowing Kenedy too much room to bypass two challenges within the first minute of the game before he fired a fierce shot into the corner.
In a frantic opening ten minutes, Neil's team did have passages of their own - Cameron Jerome shrugged off Ivanovic but his pass towards Hoolahan wasn't accurate enough, before Jonny Howson saw an effort deflect off City's striker and divert behind for a goal-kick.
Howson's booking for a heavy challenge on Oscar encapsulated the tempo of the match, a game that City were more than playing their part in despite the very early setback.
Jerome looped a header just over Thibaut Courtois's bar from Hoolahan's cross on 17 minutes, with both teams trading blows in an entertaining first half.
Norwich were dealt a blow on 36 minutes when, following a challenge with Kenedy, Alex Tettey was forced off - the midfielder initially tried to carry on, but Gary O'Neil stepped on as his replacement.
The home crowd were fired up five minutes before half-time when Courtois picked up what appeared to be a Gary Cahill backpass, but referee Lee Mason waved play on.
City's luckless half was compounded in stoppage time when Chelsea got their second - Costa was in an offside position as he picked up a through ball, but the flag stayed down and the Spain striker chipped over Ruddy and in.
HALF-TIME: Norwich City 0-2 Chelsea
Eight minutes into the second half, City's should have pulled one back when Russell Martin headed back across goal to Jerome, but the striker lofted his volley over Courtois's bar from close range.
Jerome was joined in attack by Dieumerci Mbokani with half an hour left as Neil replaced a defender with a striker, but they needed a goal quickly to spark hopes of a comeback.
It came on 68 minutes - Hoolahan bagged another assist for the season as he slid the perfect ball through to Redmond in the channel, and City's winger fired it into the roof of the net to halve the deficit.
The home crowd were urging their team to try and find the leveller, but there was another stoppage when O'Neil and Robbie Brady clashed in midair, leaving the former with heavy bleeding.
Both were able to continue after substantial medical treatment, but it left the Canaries with only ten minutes of normal time remaining.
Chelsea regained some control of the game and Nemanja Matic flicked a corner narrowly over Ruddy's bar before Redmond went close up the other end after losing three Chelsea defenders and whistling a left-footed effort wide.
Despite throwing all their effort into the cause, City left empty-handed at the final whistle - with a tantalising relegation clash with Swansea City their focus on Saturday.
FULL-TIME: Norwich City 1-2 Chelsea
GOALS: Canaries: Nathan Redmond (68) - Blues: Kenedy (1), Diego Costa (45)
NORWICH CITY: Ruddy; Bennett (Mbokani 60), Martin (c), Klose; Pinto, Tettey (O'Neil 36), Howson, Brady; Redmond, Hoolahan, Jerome. Subs not used: Rudd (GK), Jarvis, Dorrans, Mulumbu, Olsson.
CHELSEA: Courtois; Azpilicueta, Ivanovic (c), Cahill, Kenedy (Rahman 69); Fabregas, Matic; Traore (Willian 60), Oscar (Mikel 60), Hazard; Costa. Subs not used: Begovic (GK), Pato, Remy, Loftus-Cheek.
REFEREE: Lee Mason
GOLDEN GOAL TIMES: 00:39, 45:00, 67:26.