LONDON - Manchester City enjoyed a huge let-off in their quest for a top-four finish in the Premier League while Arsenal edged to within a point of fourth-placed Liverpool with an impressive victory on Saturday.

A freakish penalty 'miss' by Leicester City's Riyad Mahrez at the Etihad Stadium allowed Manchester City to squeeze out a 2-1 victory that lifted them to third place, above Liverpool.

Mahrez beat Willy Caballero with 13 minutes remaining but had slipped in his run-up and inadvertently struck the ball twice, once with each foot.

Eagle-eyed referee Robert Madley correctly applied the law and City breathed deeply before seeing out the remainder of the game to stay on course for Champions League qualification.

"When I saw the reaction from Willy, I understood immediately that it was two touches," City manager Pep Guardiola, whose side finish with matches against West Bromwich Albion and Watford, told reporters.

"The referee was so brave in making the decision. I've seen that happen before, a long time ago! It's not normal to see something like that, but it is what it is."

With Chelsea having wrapped up the title on Friday and Sunderland and Middlesbrough already relegated, the final flurry of matches will decide which two clubs join the champions Tottenham Hotspur in the Champions League and who becomes the third side to slide through the trapdoor.

Arsenal maintained their late challenge with a classy 4-1 victory at Stoke City to keep the pressure on Liverpool who now sit just one point above the in-from Gunners.

Olivier Giroud's brace and goals from the brilliant duo of Alexis Sanchez and Mesut Ozil sealed an emphatic victory for Arsenal who have won five of their past six games to jump right back into contention.

"We had a difficult week but we've won convincingly so the focus is there, the fighting spirit is there and we're pleased to win," manager Arsene Wenger told the BBC.

"I believe when the team plays well we have the right individual talent to win. We just have to win our games."

Peter Crouch scored Stoke's solitary goal -- though appeared to convert the ball with his hand.

For much of a season in which they sacked two managers, Swansea have looked destined to return to the second tier after a five-season stay in the top flight.

But under Paul Clement they have improved dramatically and Saturday's 2-0 victory at hapless Sunderland means they will be safe if Hull City lose to Crystal Palace on Sunday.

Fernando Llorente and Kyle Naughton were both on target for the Swans who have 38 points with one game left, the same as Crystal Palace who have a superior goal difference.

"It's a huge result for us. We've got ourselves into a strong position but the season is not over and we don't think it is done. Now have to look to next week," Clement said.

In the battle for south coast bragging rights Southampton beat Middlesbrough 2-1 on Saturday with goals by Jay Rodriguez and Nathan Redmond keeping them above Bournemouth who beat Burnley 2-1 thanks to Joshua King's late winner.

Southampton are ninth and Bournemouth 10th with both clubs on 45 points. City, who have 72 points to Liverpool's 70 and Arsenal's 69, have their destiny firmly in their own hands although there were nerves aplenty against Leicester.

David Silva scored a controversial opener, allowed to stand despite Raheem Sterling apparently being offside and interfering with play, before Gabriel Jesus' penalty.

Shinji Okazaki's stunning volley just before halftime re-energised Leicester though and City could have had few complaints had Mahrez's penalty earned the visitors a draw.

Liverpool play West Ham United on Sunday.

Agencies