The Egyptian forward produced a stunning assist for Cody Gakpo's opening goal in the 12th minute, cutting in on his left foot inside the box and curling an inch-perfect cross to the Dutchman.
Salah converted a penalty with 12 minutes left to play and proved once again that he can be relied upon in the biggest moments.
The result means that Liverpool have extended their lead at the top of the Premier League table to nine points, and are 11 ahead of Pep Guardiola's City, but fans have been worried about the forward's future given he has less than a year to run on his contract.
Speaking to Sky Sports after the game, Salah said that he is more than aware that the match could be his last against Guardiola at Anfield, saying: "Until now this is the last Man City game I will play for Liverpool.
"The atmosphere was incredible so I will enjoy every second here. Hopefully we just win the league and will see what will happen."
Salah's form
Salah has been in scintillating form under Arne Slot, and his outing on Sunday was the 36th time that he has registered a goal and an assist in a single Premier League match, equalling Wayne Rooney and becoming the joint leader in that stat.
In fact, the attacker has scored 11 goals and produced seven assists, the most of any player in the division.
For context, Luis Diaz has the second most goal contributions for Liverpool in the league with five goals and two assists.
The Egyptian is also averaging more goals, more goal involvements and a higher dribble success than he did under previous manager Jurgen Klopp.
Salah clearly understands his importance to the team, and when he was told that his assist to Gakpo for the opener was excellent, the forward responded: "Yeah, I'm a good player!"
Can Salah fire Liverpool to the title despite contract uncertainty?
In the aftermath of Liverpool's 3-2 win against Southampton on November 24, Salah sparked debate when he said that he was "more out than in" in regard to his future at the club.
Reds legend Jamie Carragher labelled his comments selfish, and suggested that the noise around his the Egyptian's unresolved contract situation could prove to be a distraction.
However, with Slot's side having beaten European champions Real Madrid last Wednesday and Premier League champions Man City on Sunday, the team does not appear to be distracted in any way.
The Dutch manager has won 18 of his 20 games in charge, and has so far made a mockery of those that suggested his team would falter when coming up against supposedly more difficult opponents.
Liverpool look set to challenge on all fronts this season, and fans will hope that Salah can spearhead the club to another win on Wednesday when they take on Newcastle United in the Premier League.