Chelsea are not dismissing opponents with quite the same mouth-watering panache as Manchester City, or even drawing as much focus in the title race as a resurgent Liverpool. They are not even watertight on home territory these days, always offering opponents a hint of reward. Yet, for all Maurizio Sarri’s public utterances to the contrary, they are a side refusing to believe this is merely a two-team title race.

This was an impressive victory not least because Chelsea were challenged for periods, and even pegged back to parity, but they never panicked. It helped they could send on Eden Hazard from the bench in the aftermath of Crystal Palace’s equaliser to provide an assist within 91 seconds of his introduction, but their dominance through the last half-hour was total. Álvaro Morata would have finished with a hat-trick had he not taken the bold decision to attempt to chip Wayne Hennessey, at 6ft 6in, from point-blank range in stoppage time. The goalkeeper plucked that effort from the sky, but the damage had long since been inflicted.

Sarri equalled a Premier League record here by extending his unbeaten start in the division to 11 matches, and it is the Italian’s team who are sandwiched between the more fancied contenders at present. It is already hard to believe that Chelsea finished 30 points behind City last time round.

“At the beginning, we knew very well that there was a gap,” said the head coach. “So, at the moment, we need only to try to recover the large part of this gap. I hope to recover almost all the gap, but I don’t know … It’s very difficult to recover 30 points in six months, but we are trying.”

Those efforts have been impressive to date. It is of benefit that Morata’s confidence is returning, for all the late miss as he and two team-mates tore at Patrick van Aanholt, alone in Palace territory, after the visitors’ corner was cleared. The Spaniard’s spell in English football has largely been underwhelming, a flurry of early goals aside. But the last six games have yielded five to suggest a revival. There was class to his collection and conversion on the turn just after the half-hour mark after Pedro, so often the injection of energy this team requires, had twice fizzed crosses into the centre. When Hazard’s second-half free-kick veered across the penalty area with Palace unable to muster a touch, the 26-year-old was alone at the far post to guide a low shot across Hennessey and into the far corner.

“He’s a little bit fragile, from the mental point of view,” said Sarri of Morata, once a club record £57m signing from Real Madrid. “But he’s very young and has great potential. He can improve very fast. Álvaro already improved the last month: improved for the confidence, improved for the personality, improved also from the technical point of view.

“Now he’s able to play more with the team. But I think, also, that Álvaro has a very great physical and technical potential, so I think he can improve more. For him, goals have to be the consequence [of the hard work]. He has to play for the team, with his teammates, without thinking about goals. Goals are usually consequence of teamwork.”

Nothing summed that up better than Chelsea’s third, courtesy of Marcos Alonso’s trademark burst down the left and low centre which Pedro finished on the charge from around the penalty spot. Palace, competitive for an hour, were helpless to stifle such dynamism.

The last 20 minutes were played out with the home side’s work long since done, and thoughts already drifting to Bate Borisov in midweek – where many of this side can expect a breather – and Everton on Sunday.

Palace have more wounds to lick ahead of a collision with Tottenham on Saturday, with this an occasion to sum up their season to date. Theirs had been the brighter start, when Max Meyer and Wilfried Zaha were wriggling peskily through Chelsea’s defence, only for a lack of a natural goalscorer in their ranks to leave them blunt. They had steeled themselves at the break, “to be more in their faces”, according to Andros Townsend, and duly conjured a riposte from nothing. James Tomkins’ slide-rule pass found the winger, who exchanged passes with James McArthur and, gliding past David Luiz, crunched a low shot beyond Kepa Arrizabalaga to register a first goal in 20 Premier League games.

Regardless, Hazard’s introduction would send a ripple of apprehension through Palace’s ranks, and they were overwhelmed in what time remained. They have not won in six top-flight games, stretching back to mid-September, and visit Manchester United after the match against Spurs. “But it doesn’t really matter where you are at Christmas,” said Roy Hodgson. “We were rarely outside the relegation zone last season but ended up 11th, and only outside the top half on goal difference.

“We’ve missed chances, yes, and been a bit unlucky, yes. We don’t have as many points as we should have, yes. But let’s see where we are after 38 games. It’s important to keep going irrespective of what happens in the next few games.” How he must crave a goalscorer such as Morata to ease them clear of danger.