The scoreline may give the impression Chelsea squeezed out a second successive win on their travels but in reality Maurizio Sarri’s team will not enjoy too many away victories as comfortable as this. One flash of quality was all it took to claim the spoils and, suddenly, the gap from fifth place feels more like a five-point chasm.

Given Champions League qualification had always been Sarri’s target, he remains safely on track. Not that the Chelsea manager ever really gives off the impression of being satisfied. He would depart Selhurst Park pointing to a lengthening injury list, with Olivier Giroud on crutches as he left the arena after damaging his left ankle late on, once he had finished bemoaning his players’ inability to kill off the contest long before a mildly anxious last five minutes.

His nitpicking, admittedly justified, extended to a lack of energy in the team’s movement of the ball up to the interval. But Crystal Palace had still been kept at arm’s length, and beaten more convincingly than Sarri’s grumbling assessment had implied.

Perhaps the rather downbeat nature of the occasion had affected him. This had been desperately humdrum fare until N’Golo Kanté, the manager’s half-time instructions presumably still ringing in his ears, injected some impetus early in the second half.

Chelsea had been probing, David Luiz sizing up his options in possession inside Palace’s half, when Kanté took it on himself to dart behind and away from Cheikh Kouyaté and between Patrick van Aanholt and Mamadou Sakho to the edge of the six-yard box. David Luiz’s lofted pass was perfectly weighted, with Kanté collecting neatly on his chest and steering his close-range finish beyond Vicente Guaita’s outstretched left hand.

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It was the first time Palace had conceded a goal at home since mid-November and evidence of the improvements Kanté has made to date as the World Cup winner adapts to a slightly more advanced brief in this team’s midfield. A third league goal already represents a personal best for an entire season.

“But it was his movement without the ball that was really very good, and done with the right timing,” Sarri said. “It’s very important to have that when we have to play against opponents whose block is very low, and against whom our strikers and wingers find it hard to see space.” That decisive burst between otherwise disciplined opponents illustrated his progress.

Chelsea had other opportunities, with Giroud twice supplying eye-catching finishes from marginally offside positions, and had left the woodwork quivering amid a sudden flurry of chances just before the interval.

Had either of those opportunities flown in then Palace would have felt aggrieved. Eden Hazard, scuttling into a rare pocket of space, had clipped his own heel 11 minutes from half-time, with the referee awarding a generous free-kick. Willian struck that on to the outside of a post as Guaita dived, with the referee compounding his earlier error by spying a non-existent touch from the goalkeeper.

Willian would test the Spaniard again from distance at that set piece, forcing a second corner from which Ross Barkley, having shoved James McArthur away, acrobatically flicked a shot on to the same upright with his back to goal. Yet that excitement was utterly out of character with everything mustered up to then, and plenty thereafter. Chelsea, despite their blanket possession, found it hard to prise open obstinate opponents. Palace, for their part, were toothless and lacked anything approaching incision of their own.

Roy Hodgson bristled at mention of his team’s five-goal tally from 10 home games. They have created plenty of chances – albeit not many of them clear-cut – in those fixtures, and had made 31 attempts without reward at Selhurst Park against Cardiff on Boxing Day. Christian Benteke’s absence through injury has hampered them severely but they should still be capable of better than this.

Connor Wickham was flung on just past midway through the second half and skied a half-volley over the bar in the final minute, their clearest sight of goal all afternoon, but the striker is still horribly ring-rusty after a lengthy absence through injury. He is not ready to start Wednesday’s match at Wolves.

At least Dominic Solanke, the former Chelsea youngster who has found opportunities beyond him at Liverpool, should complete a loan move later this week to offer some much needed clout.

“He’s a proven goalscorer through all the age groups at Chelsea and England,” said Hodgson, who had watched Solanke’s progression through the national ranks with interest. “If he comes here, it’ll be up to him to show he can do that in Premier League football, too. But he’s someone with the profile and ability we’re looking for.”

Until they find a way of unsettling resolute opposition, their campaign will be a prolonged flirtation with relegation. This was a disappointing way for their year to fizzle out.

For Chelsea, looking up again rather than at Arsenal over their shoulder, the future feels promising again.