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.
Juergen Klopp's side, chasing their maiden title in the Premier League era and first in the top flight in 30 years, took a 14th-minute lead from a Virgil van Dijk header but had to wait until stoppage time to put the game to bed through Mohamed Salah.
A round-up of Saturday's action in the Premier League.
Barcelona coach Ronald Koeman has joined other managers in lashing out at the packed European football calendar after deciding to rest Lionel Messi for Tuesday's Champions League trip to Dynamo Kyiv.
Winter returned to Anfield on Friday but while the temperature dropped, the standards of Juergen Klopp's side certainly did not as Sadio Mane and Mohamed Salah both struck twice in a 5-0 thrashing of relegated Huddersfield Town.
Liverpool's bandwagon rolled on as they crushed Merseyside rivals Everton 5-2
Tottenham Hotspur reached the semi-finals of the Champions League on away goals after a 4-3 (aggregate 4-4) defeat to Manchester City in a breathtaking quarter-final second leg game on Wednesday.
Liverpool survived a late spell of Everton pressure to stretch their record unbeaten run in Merseyside derbies to 17 games
Chelsea kept alive their remote Premier League title chances with a 2-0 win over London rivals Tottenham Hotspur on Sunday, set on their way by an exquisite strike from Hakim Ziyech which was quickly followed up by a Thiago Silva header.
This time Liverpool are at home, and victory would put them nine points clear.
Manchester City needed a second-half penalty from striker Erling Haaland to break the resistance of a dogged Crystal Palace.
'It wasn't just one save -- he had a lot of things to do and did it so coolly and calmly. Still he did it, incredible, unbelievable, never saw anything like it'
The reigning champions have won 53 and drawn 11 of those 64 games, scoring 169 goals and conceding 42 for a total of 170 points.
Memphis Depay scored one goal and put in an exhilarating all-round display as the Netherlands outclassed Germany 3-0 in their UEFA Nations League clash.
IMAGES from the EPL matches played on Saturday
IMAGES from EPL matches played on Sunday.
Liverpool manager Juergen Klopp acknowledged that they would have to defend better in the visit to Stamford Bridge to stop Eden Hazard reprising the sort of solo brilliance that propelled Chelsea to victory at Anfield on Wednesday.
Roberto Firmino struck a stoppage-time winner as Liverpool beat Paris St Germain 3-2 at Anfield on Tuesday after Kylian Mbappe looked to have secured a point for the French side in a compelling Champions League Group C clash.
Images from Saturday's action in the Premier League.
An extra-time goal from Roberto Firmino gave Liverpool a 1-0 victory over Brazil's Flamengo to win the Club World Cup at the Khalifa International stadium on Saturday. It is the first time Liverpool have won the competition, which features each continent's champions, and they became only the second English team to lift the trophy after Manchester United in 2008.
News of all that's transpired on and off the football field
Talking points from this weekend's Premier League action as top two Manchester City and Liverpool both won with City remaining a point clear with two games remaining.
Liverpool opened up an eight-point lead at the top of the Premier League with an emphatic and hugely impressive 3-1 win over defending champions Manchester City.
Round-up of World Cup qualifiers played on Friday
Cristiano Ronaldo may have played his last game for Real Madrid after winning a fourth Champions League crown with the Spanish side in a 3-1 victory over Liverpool on Saturday, saying he would soon make an announcement on his future.
A preview of the line-up action in the English Premier League
IMAGES from the EPL matches played on Wednesday
Barcelona coach Ronald Koeman has defended centre-back Gerard Pique's right to make comments about referees favouring Real Madrid.
Images from Premier League matches played on Wednesday.
IMAGES from the English Premier League match played between Manchester United and Liverpool at Old Trafford on Saturday
A round-up of the action in the English Premier League on Monday.
FIFA World Cup set pulses racing and ended with a young, exciting France team clinching the title.
Unbeaten Liverpool have 45 points from 17 games with champions Manchester City, who beat Everton 3-1 on Saturday, a point behind.
IMAGES from English Premier League matches played on Sunday
Manchester United have signed Leicester City's England centre back Harry Maguire on a six-year contract, the Manchester club announced on Monday.
Premier League champions Liverpool maintained their 100 per cent start to the season with a 3-1 win against Arsenal at Anfield on Monday leaving them level on nine points with pacesetters Everton and Leicester City.
Liverpool had to be satisfied with a 1-1 Premier League draw at Arsenal on Saturday as their usually prolific attacking trio were well shackled by their improving hosts.
Reports in British media put the latest bid at 125 million euros.
Tottenham Hotspur and Liverpool raised the spirits with a rip-roaring 2-2 draw in a pre-Christmas Premier League classic on Sunday after a weekend marred by COVID-19 related postponements.
Images from the EPL matches played on Saturday
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