LONDON (AFP) - Diego Costa's second half strike brought relief to Stamford Bridge as Chelsea halted a run of three straight Premier League defeats with a 1-0 victory over Norwich on Saturday.

It will take more to turn the reigning champions' season around, but this win at least stopped the rot and eased the pressure on manager Jose Mourinho.

There were certainly positives for Mourinho, who this week received the public backing of the club's hierarchy for the second time this season, with Costa rescuing an indifferent display with his first goal in seven games and Eden Hazard again showing signs of a return to form.

But it is clear Chelsea, who moved above Norwich into 15th position, remain a shadow of the side that dominated the title race last season as they struggled to overcome the lowly Canaries.

Mourinho maintains Chelsea's performances have been deserving of greater reward in recent weeks, particularly in the defeat at Stoke City last time out.

That has strengthened the manager's belief his side are on the verge of drawing a line under their disastrous start.

But with the gap to the top four growing ever wider, Mourinho knew his side must quickly resolve the problems at both ends of the pitch that have contributed to their demise this season.

And in the first half, the signs were the Blues are still some way short of finding the answers.

Mourinho could have no complaints with the way his side approached the game, with Cesc Fabregas and Nemanja Matic providing the midfield platform that allowed the home side to push Norwich backwards.

Less satisfactory was Chelsea's efforts inside the visitors' penalty area, with Costa in particular guilty of spurning a succession of good chances that confirmed the Spain striker is still operating way below the standards he set last season.

Coming into this game, the Brazil-born forward had scored just twice in 10 Premier League starts.

And while he had the opportunity to add to that tally before the break, his finishing lacked conviction, suggesting his confidence has been affected by Chelsea's dismal run.

Costa wasn't the only culprit in the first half with Fabregas and Willian also failing to make the most of good chances.

But more is expected from Costa and the way he shot high over the bar after being picked out by Pedro's cut-back was a sign of things to come.

A more glaring miss came in the final moments of the first half when Chelsea broke quickly with Kenedy eventually finding Costa in time and space on the right hand side of the Norwich box, only for the forward to shoot too close to keeper John Ruddy.

And prior to that, Costa failed to read Hazard's intentions when the midfielder sent a low ball across the face of goal, waiting instead for a pull-back on the edge of the box.

Mourinho's reaction on the touchline spoke volumes and the manager again remonstrated with Costa following a carbon-copy move early in the second half.

Costa produced the ideal response, however, in the 64th minute when he offered a glimpse of his undoubted quality and conjured the goal Mourinho will hope triggers a resurgence in his form.

Chelsea's pressure had been building after the break and Norwich cracked when they lost concentration as Fabregas took a quick free-kick on the halfway line.

The midfielder's chip allowed Costa to break free behind the backtracking defenders and this time the striker showed great composure to curl the ball beyond Ruddy and inside the near post.

Mourinho's side may have deserved their lead on the balance of play but Norwich could easily have found themselves ahead in the first half.

Willian was fortunate referee Craig Pawson allowed the Brazilian's clumsy challenge on Robbie Brady to go unpunished inside the area and it took an excellent block by John Terry to deny Sebastien Bassong's close-range shot.