Swansea went ahead five minutes before the break when an attempt to clear by Liverpool's 75 million pounds ($104.88 million) defender Virgil Van Dijk landed at the feet of Mawson who swept the ball home for his sixth league goal this season.
Cesc Fabregas kept alive Chelsea's hopes of finishing in the top four with a quickfire goal in a 1-0 win at Swansea City which leaves the Welsh side facing a major fight to retain their Premier League status.
Burnley reached the Europa League third qualifying round with a 3-1 win over Aberdeen after extra time at Turf Moor on Thursday but now face another tough battle to increase their squad size.
Defeat always seemed likely for West Brom, who are bottom of the Premier League and sacked their chairman and chief-executive on Tuesday.
City were not at their all-action best early on as Burnley looked comfortable at the back, but the game turned on a penalty decision that incensed the visitors when Bernardo Silva was adjudged to have been brought down by Burnley goalkeeper Nick Pope just before the half hour.
Leicester City's beleaguered manager Claudio Ranieri suggested he is ready to drop some of the players who won them the Premier League title as the Italian seeks to stave off relegation just one season later.
Images from the English Premier League matches played on Sunday
Out-battled for an hour by their modest south coast opponents, Arsenal belatedly sparked into life and Olivier Giroud's glancing header two minutes into stoppage time completed their remarkable recovery from 3-0 down.
Romelu Lukaku extended his impressive FA Cup scoring record by netting twice in Manchester United's 2-0 win at Huddersfield Town to earn Jose Mourinho's side a quarter-final tie at home to Brighton & Hove Albion.
Swansea City's hopes of salvaging their place in the Premier League suffered a potentially grievous blow as Ryan Fraser's deflected strike earned Bournemouth a 1-0 win on Saturday to secure another season of top-flight football for the Cherries.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field