Arsenal’s Alexis Sanchez (right), and Stoke City’s Glen Johnson battle for the ball during their English Premier League soccer match at the bet365 Stadium, Stoke-on-Trent, England, on May 13. (AP)

LONDON, May 13, (AFP): Alexis Sanchez shone and then succumbed to injury as Arsenal won 4-1 at Stoke City on Saturday to close in on the Premier League top four.Sanchez teed up Mesut Ozil for Arsenal’s second goal and scored their third – his 50th Premier League goal – after Peter Crouch had brought Stoke back into the game with a controversial handball goal.Arsene Wenger’s side are now a point behind Liverpool, who occupy the fourth and final Champions League spot, and three points below third-place Manchester City, who beat Leicester City 2-1.Liverpool have played the same number of games as Arsenal and look the team the most susceptible to be overtaken by Wenger’s men, who now have the same goal difference.Liverpool visit West Ham United on Sunday and host relegated Middlesbrough on the final day, while Arsenal host relegated Sunderland on Tuesday and finish the campaign at home to Everton.Wenger saw his team take a 42nd-minute lead at the bet365 Stadium when Hector Bellerin’s low cross was tapped in by Olivier Giroud.An exquisite pass by Sanchez released Ozil to dink in Arsenal’s second goal 10 minutes into the second half.Substitute Crouch brought Stoke back into the game in the 67th minute when he used his forearm to propel Marko Arnautovic’s left-wing cross past Petr Cech at the near post.But Sanchez settled fluttering Arsenal hearts by arrowing a shot into the bottom-left corner before departing, having apparently sustained a thigh injury.His replacement, Aaron Ramsey, set up Giroud to net Arsenal’s fourth goal with 10 minutes remaining.Fortune favoured Manchester City as they overcame outgoing champions Leicester at the Etihad Stadium.David Silva’s 29th-minute opener was awarded despite an apparent offside against Raheem Sterling, while Riyad Mahrez had an equalising penalty disallowed after he slipped and struck the ball twice.Gabriel Jesus doubled City’s lead from the penalty spot, with Shinji Okazaki halving the deficit by hooking a stunning volley into the top-right corner.“We need one more game to be in the top four, but it’s in our hands,” said City manager Pep Guardiola, whose side host West Bromwich Albion on Tuesday.“West Brom will be tough, but hopefully we can be better than today.”Mahrez won a 77th-minute penalty after luring Gael Clichy into a clumsy foul, but despite him sending the ball past Willy Caballero, eagle-eyed referee Robert Madley ruled it out.“To the letter of the law it’s a double touch, but he could bring it back for an encroachment from Manchester City, so there’s a bit of injustice,” complained Leicester manager Craig Shakespeare.Swansea City took a big step towards safety after goals from Fernando Llorente and Kyle Naughton secured a 2-0 win at Sunderland that moved them four points clear of the bottom three.“It’s a huge result for us,” said Swansea manager Paul Clement, whose side host West Brom on the season’s final day.“We’ve got ourselves into a strong position, but the season is not over and we don’t think it is done.”Third-bottom Hull City trail Swansea by four points and will be all but relegated if they do not win at Crystal Palace – who are level on points with Swansea – on Sunday.Southampton added to the doom and gloom at Middlesbrough with a 2-1 win at the Riverside Stadium that lifted Claude Puel’s side up to ninth place.Jay Rodriguez and Nathan Redmond netted superbly taken goals for Saints, with former Chelsea striker Patrick Bamford reducing the arrears for Boro with a 73rd-minute header.Bournemouth climbed to 10th after Josh King’s 85th-minute goal – his 16th of the campaign – snatched a 2-1 home win over Burnley.