Salah's sublime second-half strike leaves Liverpool on 67 points, three ahead of second-placed Arsenal and four ahead of City on a pivotal day in the title race.
Tottenham Hotspur and Newcastle United both sealed comeback victories to boost their European qualification hopes.
Liverpool hammered Sparta Prague 6-1 on Thursday to storm into the Europa League quarter-finals 11-2 on aggregate.
Tottenham Hotspur hammered 10-man Aston Villa 4-0 in the Premier League on Sunday thanks to four second-half goals, allowing them to close the gap with their Birmingham rivals to two points in the chase for Champions League football next season.
An early penalty by Alexis Mac Allister and a Darwin Nunez brace helped Liverpool to thrash Sparta Prague 5-1.
Brazilian Casemiro struck late to send Manchester United into the FA Cup quarter-finals with a 1-0 victory over Nottingham Forest as teenagers Jayden Danns and Lewis Koumas inspired Liverpool to a 3-0 win over Southampton on Wednesday.
Manchester City and Arsenal closed in on Premier League leaders Liverpool with contrasting victories on Saturday as Manchester United's bubble was burst by Fulham.
Liverpool draw Sparta Prague in Europa League last 16
IMAGES from the Premier League matches played in England on Sunday.
Bukayo Saka scored either side of halftime as Arsenal crushed second-bottom Burnley 5-0.
Chelsea came from behind to beat Crystal Palace 3-1 thanks to added time goals from Conor Gallagher and Enzo Fernandez.
Liverpool reclaimed top spot in the Premier League with a 3-1 win over Burnley at Anfield on Saturday, but they were made to battle hard by a brave visiting side.
IMAGES from the Premier League matches played on Saturday.
Arsenal closed the gap on leaders Liverpool with a 2-1 Premier League victory at Nottingham Forest
Vitaliy Mykolenko's 39th-minute own goal had put Luton ahead before Jack Harrison cheered the Everton faithful with an equaliser in the 55th minute, hammering in a low shot that Luton keeper Tim Krul allowed to let slip through his hands.
Luton Town knocked out Everton and sixth tier Maidstone United upset Championship Ipswich Town
Brighton midfielder James Milner, who made his Premier League debut in 2002 at age 16, passed Ryan Giggs into second in all-time league appearances on Monday with 633 matches. He needs 20 more to equal Gareth Barry's record.
Third-placed Aston Villa are the surprise package of the season and Unai Emery's side face relegation-threatened Burnley while fifth-placed Spurs host a resurgent Bournemouth who have 19 points from their last seven games.
Arsenal had more than twice as many chances but failed to take any as the visitors defended gamely.
Manchester City climbed back into the Premier League's top four as second-half goals by Phil Foden, Julian Alvarez and Bernardo Silva sealed a comeback 3-1 victory at Everton on Wednesday.
A summary of Sunday's action in the English Premier League.
Rennes denied late Europa League equaliser due to little-known rule
IMAGES from the Premier League matches played on Saturday.
IMAGES from the Premier League matches played on Wednesday.
Images from the English Premier League matches played on Sunday night.
IMAGES from Saturday's action in the English Premier League.
IMAGES from the Europa League matches played on Thursday.
A summary of Saturday's action in the English Premier League.
English Premier League leaders Manchester City and Chelsea slugged out a magnificent 4-4 draw at Stamford Bridge.
Brighton secured their second victory of the competition with a comfortable win at Ajax thanks to goals from Ansu Fati and Simon Adingra.
Manchester City roared back to the top of the Premier League with a 6-1 thrashing of Bournemouth after Manchester United steadied the ship
A summary of Sunday's action in the Premier League.
Jose Mourinho's side top Group G with a maximum nine points, three clear of second-placed Slavia.
Images from the Premier League matches played on Saturday.
A look at how India have fared in their World Cup opening games.
Substitute Gabriel Martinelli fired a last-gasp winner to earn Arsenal a 1-0 victory over Manchester City on Sunday.
Champions Manchester City slipped to a shock first Premier League defeat of the season at Wolverhampton Wanderers on Saturday, while Manchester United's campaign of woe continued with a loss to Crystal Palace.
Images from the English Premier League matches played on Sunday
Liverpool overcame an early scare and came from a goal down to claim a 3-1 win at Austria's LASK Linz.
A summary of the UEFA Champions League Group Stage action, on Wednesday.
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