Jan 1 (Reuters) - West Ham United began the new year in the same manner as they saw out the last, with an impressive away victory as they beat Crystal Palace 3-2 in the Premier League on Saturday. Manuel Lanzini scored twice at Selhurst Park, before a late rally from the home side with two late goals, as fifth-placed West Ham moved within a point of fourth-placed Arsenal. The two goals in the final minutes of the game at least gave Palace some reward for what was a positive display after they went in at the break 3-0 down despite creating several chances. West Ham are on 34 points, one more than Tottenham Hotspur and three ahead of Manchester United although both those teams have two games in hand. David Moyes" side, the surprise package of the season, took the lead in the 22nd minute with Michail Antonio sliding in to poke home a wonderful cross from Said Benrahma. Three minutes later, the Hammers made it 2-0 with an outstanding finish from Lanzini, who flicked the ball to his left foot and volleyed home after good work from Declan Rice. Lanzini made it three just before the break, drilling home a penalty after a VAR review found that Luka Milivojevic had handled in the box. Palace got a goal back in the 83rd minute when Odsonne Edouard stretched to turn in a fine cross from substitute Michael Olise who then scored himself in the 90th minute with a free-kick. Patrick Vieira"s side had hit the woodwork twice in the first half and enjoyed the bulk of possession and Antonio was generous in his praise of Palace. "To be fair this season Crystal Palace are playing unbelievable football. The way their gaffer has them playing is quality," he said. "All game they were after us but when opportunities dropped for us we took them. They managed to get two and we had to hold out. You saw the pressure they put us under but we managed to hold out and it"s three points to start the year," he added. The meeting between the two sides in August had ended 2-2 and Palace defender Joachim Andersen said it was hard result to take. "We"ve played West Ham two times now and both times we have dominated them. I think we should win this game easy. They had two chances and a penalty which isn"t a penalty. We should win this game," he said.