The win moved Liverpool level with City on 86 points in the standings
Salah, 25, struck four goals in Liverpool's 5-0 thrashing of Watford that lifted them back into third place in the Premier League on Saturday.
Their work in the transfer market has also added to the positivity around the club after German manager Juergen Klopp made some major moves that have clearly strengthened his squad.
Diogo Jota and Mohamed Salah were on target as Liverpool edged Premier League strugglers Nottingham Forest 3-2.
Egypt's talisman scored a consolation penalty as he started his first World Cup game in Group A after recovering from the injury suffered in last month's Champions League final but made little other impact in a match his side needed to win.
Salah not risked as Egypt elect to look ahead after Uruguay loss
Images from Premier League matches played on Wednesday.
Real Madrid and Croatia midfielder Luka Modric was voted Player of the Year for last season by European soccer body UEFA on Thursday, ahead of Cristiano Ronaldo and Mohamed Salah with Lionel Messi fifth.
Manchester City took a slender lead from the first leg of their Champions League quarter-final after Kevin De Bruyne's 70th minute goal earned them a 1-0 win over Atletico Madrid at the Etihad Stadium on Tuesday. In anothr match, Liverpool took a firm grip of their Champions League tie with Benfica as goals from Ibrahima Konate, Sadio Mane and Luis Diaz earned them a 3-1 victory in Lisbon.
Manchester City came from behind twice to earn a 2-2 draw with Liverpool in a breathless and pulsating Premier League encounter, at Anfield, on Sunday. All four goals came in the second half.
Roma didn't expect that Salah and Liverpool would stand between them and a place in the Champions League final.
Brighton kept a disciplined formation, frustrating Liverpool and as the second half wore on the home side began to lose their fluency.
Late goals by Mohamed Salah and Jordan Henderson earned Liverpool a crucial 3-1 victory at Southampton to move them back to the top of the Premier League on Friday.
Salah was seen with controversial Chechnya leader Ramzan Kadyrov while he was recuperating from the shoulder injury he suffered during the Champions League final.
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 summary of Sunday's action in the Premier League.
Manchester City now need, at most, 11 points from their remaining seven matches to secure their third Premier League title in four seasons.
A round-up of Saturday's action in the Premier League.
Sky reported Manchester United, Manchester City and Chelsea have been in touch with Kane's representatives.
Russia face Egypt in their second match in St Petersburg on Tuesday after a resounding 5-0 victory over the Saudis that has catapulted them to the top of Group A, ahead of Uruguay on goal difference.
Uruguay's Jose Gimenez scored with a thunderous 89th minute header to deal Egypt a 1-0 defeat in their World Cup opener on Friday, just as the North Africans appeared to have escaped with a point despite missing key striker Mohamed Salah.
Liverpool's Champions League winning trio of Mohamed Salah, Virgil van Dijk and Sadio Mane joined regulars Cristiano Ronaldo and Lionel Messi on the shortlist for The Best FIFA Men's player award
Lionel Messi said he never expected to have such a successful career after receiving his fifth Golden Shoe, on Tuesday, for being the top goalscorer in Europe last season.
'This award is not just mine.' 'It is my team mates' from Real Madrid and Croatia.' 'Without my coaches, I would not have won this and without my family I would not be the player I am today.'
Images from Saturday's action in the Premier League.
'I'm very excited to be here. I'm very happy'
Only two teams -- Chelsea in 2005-06 and Manchester City last season -- have had more points after 18 Premier League games in a season than Liverpool's 48.
The Reds have won 28 of their 31 Premier League matches this season.
Images from Saturday's action in the Premier League.
Images from Sunday's English Premier League matches.
Liverpool will play the winner of Wednesday's other semi-final between Ajax Amsterdam and Tottenham Hotspur with the Dutch side leading 1-0 from the first-leg in London.
A round-up of Tuesday's action in the UEFA Champions League.
A round-up of Sunday night's matches in the Premier League.
Photos of the Champions League matches played on Tuesday.
Chelsea paid a heavy price for a 3-2 defeat at West Ham United as first Liverpool, then Manchester City, leapfrogged them in the English Premier League title race on Saturday, with City ending the day on top for the first time this season.
Images from Saturday's action in the Premier League.
He said the treatment of women "in my culture and in the Middle East" had changed his opinions on gender issues.
Egypt striker Mohamed Salah was voted as the African Footballer of the Year for the second successive year at the Confederation of African Football's awards ceremony in Dakar on Tuesday.
Liverpool's Mohamed Salah ended his Premier League goal drought in style by scoring twice as the champions raided the capital again to crush West Ham United 3-1 on Sunday.
Russia got their World Cup campaign off to a dream start with a 5-0 thumping of Saudi Arabia but face an entirely different beast in the form of Egypt, who should be revitalised by the return of their talismanic striker Mohamed Salah.