This was the kind of ruthless performance that has defined David Moyes’s second spell at West Ham. In front of a raucous New Year’s Day home crowd and against opponents who clearly fancied their chances of bloodying the noses of their London rivals, two brilliant first-half goals from Michail Antonio and Manuel Lanzini – and Luka Milivojevic’s helping hand – ensured that their Champions League dream remains alive and well despite a late Crystal Palace fightback. Had Jean-Philippe Mateta’s last-gasp volley sailed the other side of the post then it could have been a different story but with more than half the season completed, West Ham find themselves within a point of Arsenal and one ahead of Spurs, albeit having played two games more than Antonio Conte’s side. Anyone who had already written them off after their mini-blip last month may have to think again. “It was never comfortable but at this time of the year you take what you get,” said Moyes. “I’m thrilled with us getting these results but we need to get back to being mean and not letting teams have opportunities against us.” Patrick Vieira had been given a warm welcome from the home supporters as he returned from his Covid-enforced two-match absence. Yet the hosts had to do without Wilfried Zaha and Cheikhou Kouyaté as both were isolating ahead of their scheduled departure for the Africa Cup of Nations. That meant a return for Milivojevic in midfield, while West Ham welcomed back Declan Rice from suspension. Despite their stuttering form before Christmas, West Ham’s hopes of finishing in the top four should remain realistic as long as Rice is in the side but Moyes will also know finding defensive reinforcements in the January market could prove vital. They should really have found themselves behind inside the first two minutes when Jordan Ayew’s cutback picked out Jeffrey Schlupp but the Ghanaian somehow managed to hit the post from close range. When Ben Johnson was called on to block another effort from Schlupp, it seemed only a matter of time before Palace found the breakthrough. But having weathered the initial storm, West Ham went 2-0 up after some smart finishing from Antonio and Lanzini. There was nothing Vicente Guaita could do about either: West Ham’s top scorer only had to touch Saïd Benrahma’s wicked inswinging cross to divert it in and Lanzini’s goal three minutes later, after a typically surging run from Rice, was an instinctive strike with his third touch that flew past the Palace goalkeeper. To their credit, Palace kept coming forward and should have pulled one back when Odsonne Édouard let fly after being set up by Ayew, only for his shot to cannon back off the bar. Christian Benteke did at least manage to hit the target twice in quick succession but found Lukasz Fabianski in top form. Yet it was a moment of utter madness in first-half injury-time from Milivojevic that ended any chance of a Palace comeback. The Serbia midfielder probably thought he was being clever when he clearly handled the ball on the blind side of the referee, Darren England, and seemed to have got away with it initially. Unfortunately for him, VAR had spotted that the infringement had taken place just inside the box and it was left to Lanzini to stroke home his second from the spot. Vieira left the pitch at half-time remonstrating with a bemused England and was shown a yellow card after continuing his protestations at the final whistle, even if he later acknowledged it had been the correct call. “You have to give them credit. When they had the chances, they took them,” said the Palace manager. “We had a couple we did not take. We are learning in a hard way.” An early sighter from Benrahma at the start of the second half could have given Palace even more of a mountain to climb. Ayew – who will now meet up with Ghana’s Afcon squad – was the one constant threat down the right flank and his ball across the area could have given them a lifeline had Édouard been able to direct his shot on target. Milivojevic’s miserable evening came to an end when he was replaced by Mateta with more than half an hour to play, while Antonio went close to doubling his tally with a shot from just outside the box. Michael Olise – another substitute – was the architect of Palace’s fightback when his excellent cross was tapped home by Édouard at the far post before he curled home a free kick to set up a tense finale. But it came just too late to throw Moyes and his side off course.