London, April 2 : Manchester City kept their calm after falling behind, to roar back and beat Liverpool 4-1 in a result that very much keeps them in the race for the Premier League title. Although Mohamed Salah poached a goal for Liverpool in the 17th minute, Julian Alvarez, who was in the side for injured Erling Haaland, levelled 10 minutes later and then helped Riyad Mahrez set up Kevin de Bruyne to put City ahead in the first minute of the second half. Ilkay Gundogan then put the result beyond doubt when he made it 3-1 in the 53rd minute after Alvarez's shot had been blocked and the impressive Jack Grealish got the goal he deserved in the 74th minute after exchanging passes with De Bruyne. "When we conceded the goal, we were playing really well. Of course, they are always a threat in the transitions, but we played really well in all departments. It was one of our best performances in these seven years," said Man City coach Pep Guardiola afterwards. Arsenal responded magnificently to the pressure with a 4-1 win at home to Leeds United, with two goals from a fit-again Gabriel Jesus (the first from the penalty spot), while Ben White and Granit Xhaka completed the scoring for Arsenal. Goals from Ollie Watkins and John McGinn gave Aston Villa a 2-0 win away to Chelsea to once again pile the pressure on coach Graham Potter, who had to endure chants of "you don't know what you're doing" from the fans in Stamford Bridge. Aston Villa, meanwhile, climbed up to ninth after a run of four wins from their last five league games. Roy Hodgson's return to Crystal Palace ended in dramatic fashion with Jean-Philippe Mateta giving Palace their first win of 2023 with the very last kick of the game. Ricardo Pereira had put Leicester ahead in the 56th minute, but Daniel Iversen's own goal from an Eberechi Eze free-kick levelled the score three minutes later. Jean-Philippe Mateta sent home Jordan Ayew's assist in the 94th minute and pushed Leicester into the bottom three with 25 points from 28 games. Bournemouth came back from a goal down to beat Fulham 2-1 and climb out of the relegation zone. Andreas Pereira put Fulham ahead early in the game, but second-half strikes from Marcus Tavernier and Dominic Solanke, with Tavernier scoring a brilliant goal, turned the game around. Daniel Podence scored a late equalizer to save a point for Wolves in a relegation dogfight away to Nottingham Forest, who looked to be on the way to three vital points after a first-half strike from Brennan Johnson. Alexis Mac Allister's 90th-minute penalty saved a point for Brighton in a thrilling 3-3 draw at home to Brentford. Allister's spot kick was the third time Brighton came back from a goal down in the match. /IANS