Chelsea took the lead before some fans had even taken their seats when Kenedy drove a low left-shot shot into the far corner of John Ruddy's net from just outside the area after jinking past two defenders having been fed by the marauding Eden Hazard.
Diego Costa made it 2-0 to the visitors on the stroke of halftime when he clipped the ball over Ruddy from close range after being found inside the box by Bertrand Traore, although the Spain striker appeared offside when he received the pass.
It was Costa's eighth goal in his last 10 league games for improving Chelsea who have provisionally moved within five points of fifth-placed Manchester United and, after a dreadful start to the season, are now targeting the European qualifying places.
“It's not Chelsea's standard to be happy to be out of the relegation zone, and sit back and relax a bit,” interim manager Guus Hiddink told a news conference after his side survived a late rally by the hosts after they pulled a goal back.
“We have to set new targets now with the ambition of Chelsea in the direction of Europe. We have a tight schedule... and the squad is not very, very broad... If everyone is available, we'd like to go as high as possible towards the European spots.”
Chelsea have moved up to eighth on 39 points from 28 matches but Hiddink felt they should have wrapped up the points long before Costa scored the second goal.
“I think we were a bit sloppy in the finishing in the first half. We had a splendid start through Kenedy, a beautiful goal, but after that we had some options to get a second,” he said.
“We did in the end, but we should have killed it off already by then. I'm satisfied with the result, but I like to be critical that we didn't finish it off early.”
Norwich piled on the pressure after lively winger Nathan Redmond fired a rasping drive into the net in the 68th minute but Alex Neil's side could not equalise and their seventh defeat in eight league games has seen them slip into the bottom three.
Original source: A ‘beautiful’ goal in 39 seconds