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.
With Crystal Palace dangerously close to being relegated, manager Patrick Vieira was sacked after 20 months in charge.
Should Manchester United win their next two games, the gap will be cut to four points and while only a collapse of astonishing proportions would deny Manchester City the title.
Images from Saturday's action in the Premier League.
A ninth successive win in all competitions for United was celebrated with real vigour, as they moved to within a point of City in second, giving Arsenal the chance to go eight points clear at the top of the standings with a win over Tottenham Hotspur on Sunday.
Leicester will remain second overnight with Everton, level on points with them, not playing later on Monday after their home match against Manchester City was postponed following more positive COVID-19 cases at City.
Last year's FA Cup runners-up Stoke City had a man harshly sent off but then scored a controversial penalty as they reached the quarter-finals with a 2-0 win at fourth tier Crawley Town on Sunday.
Danny Gabbidon headed in the winner as Queens Park Rangers weathered a spirited performance from third tier MK Dons to win 1-0 in their FA Cup third round replay on Tuesday and give new manager Mark Hughes his first victory.
Manchester United remain winless at home in the league this season after Arsenal enjoyed their first win at Old Trafford
IMAGES from the Premier League matches played on Sunday
The defeat halted Brighton's impressive three-game winning streak which included a 4-1 win over Chelsea and a 3-1 victory at Arsenal in the League Cup on Wednesday.
Bayern Munich wasted a two-goal lead and needed a lucky 82nd- minute winner from Joshua Kimmich to beat Borussia Dortmund 3-2 in Germany's Super Cup on Wednesday and secure their fifth title of the year.
Bruno Fernandes struck from the penalty spot in the ninth minute of stoppage time to give Manchester United victory at Brighton & Hove Albion in the Premier League on Saturday after an incredible finale.
Manchester United and Liverpool, England's two most successful clubs, will do battle in the third round of the FA Cup after the draw was made on Sunday.
Substitute Gabriel Martinelli fired a last-gasp winner to earn Arsenal a 1-0 victory over Manchester City on Sunday.
News of all that transpired on and off the football field.
IMAGES from the Premier League matches played on Tuesday.
Defeats at Manchester City and Brighton & Hove Albion had left Arsenal down in 11th place but their victory on the south coast lifted them to ninth with 43 points from 31 games -- eight behind fourth-placed Chelsea who were playing City later.
Liverpool will resume their quest for a first top-flight title in 30 years at city rivals Everton on June 21, as the English Premier League released its revised fixture list for the first three weeks of the restarted season on Friday. Liverpool are 25 points clear at the top and are two victories away from winning the Premier League, but will have a shot at securing the title by beating Everton if City lose to Arsenal.
Manchester City were bundled out of the English League Cup by League One Brighton & Hove Albion on penalties on Wednesday.
EPL's 'Project Restart' envisages a return to play in June at neutral venues, once given the green light from the government, but players are worried about transmission when sharing the pitch with others in a contact sport.
Manchester City's Sergio Aguero had said a number of players would be fearful of resuming the season amid the virus outbreak with more than 4.02 million people infected globally and over 276,000 dead.
Images from the English Premier League matches played on Sunday.
'It would be very difficult to relegate somebody, particularly from the Premier League, if the season hasn't played out'
Chelsea have completed the transfer of defender Wesley Fofana from Leicester City, both Premier League sides said on Wednesday, with the Frenchman signing a seven-year contract with the west London club.
Match-by-match facts and statistics ahead of the first round of Premier League fixtures from August 5-7 (all times IST).
Chelsea won their first competitive match under coach Mauricio Pochettino with a 3-0 home victory over Premier League new boys Luton Town.
A summary of Sunday's action in the English Premier League.
Liverpool head to United with widest gulf in years
Five talking points from the Premier League weekend:
Manchester City thrashed West Ham United 4-1 in the Premier League on Saturday to claim their first back-to-back wins since October.
Rennes denied late Europa League equaliser due to little-known rule
Images from the English Premier League matches played on Saturday
Pep Guardiola hailed Sergio Aguero's 'unique' skill of sniffing out chances in front of goal, and David Silva's ability to ghost past defenders
With United unable to sign a replacement, the pressure will be on 21-year-old England forward Marcus Rashford to deliver the goals in a more central role than he has previously operated in.
Pep Guardiola's insatiable team were already thinking beyond the magnificent 2018-19 campaign and contemplating a third straight English title win next season with the Spaniard having said they will get even better.
Manchester United languish 14th in the standings on 19 points, their worst placing to end a calendar year since they were 15th in 1989.
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 regained their place at the top of the English Premier League with a 2-0 win at Cardiff City on Sunday that restored their two-point lead over Manchester City
After bagging the League Cup, being locked in a titanic battle with Liverpool for the Premier League title and in the Champions League quarter-finals, Pep Guardiola's side remain on course for an unprecedented clean sweep.
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