Crystal Palace 0 Chelsea 3

Chelsea supporters would love to think that the second half of 2015 was simply a bad dream. Sadly for them, it was grotesquely real but the new year got under way in fine style for them and there was even evidence of their old champions’ swagger.

It was as if a switch had been flicked on the misery of the preceding months as Guus Hiddink enjoyed the first victory of his second spell as caretaker manager and Willian produced the outstanding moment of the afternoon. His stinging drive from outside the area for Chelsea's second goal was still rising when it ripped into the roof of the net.

Chelsea had started the day three points above the relegation zone and with only four teams beneath them, and a case could be made for next Sunday’s FA Cup tie at home to the League One side Scunthorpe United being the bigger game. The table looked a little bit better for them after this and, although much of the meaning has been stripped from their Premier League season, the team did look much more like their old selves.

Crystal Palace were chasing the league double over their London neighbours, having won at Stamford Bridge in August – the first real shock result of the José Mourinho implosion – but they were breached here by Chelsea’s slick football and they had no answers of their own. As confidence coursed through the visitors’ veins, Palace ran aground en route to their first defeat in seven.

It seemed destined to be Chelsea's day from the moment that Oscar gave them the lead in the 29th minute and they could even shrug off the early loss of Eden Hazard to what looked like a groin problem.

The winger had tried to carry on only to eventually plonk himself down on the turf, moments after losing out tamely to Joel Ward by the corner flag, and indicate that his game was over. Hazard was a snap-shot in loneliness as he trudged off down the sideline towards the tunnel.

Chelsea’s breakthrough goal was marked by high-end quality, which sparkled amid the gloomy weather and sparked happiness inside the travelling enclosure. “We are staying up,” the Chelsea fans chanted.

Cesc Fàbregas, back in the team after illness and at the expense of Nemanja Matic rather than Mikel John Obi, was the initial creator, sliding a ball through for Diego Costa, after the striker had spun off his marker to run in behind. Costa, the other returnee to the lineup – from suspension – cut a lovely disguised cross back for Oscar and the midfielder tapped home his fifth of the season from close range.

Hazard's replacement, Pedro, was industrious on the left and Chelsea made inroads up that side. They might have had the second in the 37th minute when Fàbregas again cut Palace apart with a ball forward, this time for César Azpilicueta. The left-back's first touch on his chest was true and, one-on-one with Wayne Hennessey from a tight angle, he was denied by a block from the goalkeeper. Kurt Zouma also missed with a free header from Willian's free-kick shortly after the interval.

The tackles flew in. Damien Delaney and Scott Dann were both booked for kicking Costa but Chelsea showed their mettle. Palace had drawn blanks in their previous two outings and the continued absence of the injured Yannick Bolasie was compounded by the loss of Yohan Cabaye to a ban for reaching five yellow cards. Both creators were missed as Palace groped for a cutting edge against a Chelsea defence that was well protected by Mikel. He kept things simple to catch the eye.

Fraizer Campbell had gone close with Palace's only first-half chance in the 26th minute, after Jason Puncheon's dangerous cross, and they flickered in the 59th minute through Wilfried Zaha. Teed up by Campbell after Chelsea had appealed in vain for a foul on Costa, Zaha's shot was scuffed somewhat and Thibaut Courtois stretched to save.

Moments later, the game was over. Willian started the move, working the ball to Fàbregas, who found Oscar. When the ball broke after Dann’s tackle, Willian strode on to it and let fly. Hennessey felt it scorch past him.

Chelsea got the third shortly afterwards when Willian teased James McArthur before shooting. Hennessey pushed it out but only as far as Costa, who bundled his effort home off Ward.

(Guardian service)