Jurgen Klopp's side have now won 11 and drawn one of their 12 league matches this season, leaving them eight clear of second-placed Leicester City and third-placed Chelsea, and nine points clear of the reigning champions City, who stay down in fourth after suffering their third defeat of the campaign.
Liverpool made the breakthrough in the sixth minute when Fabinho found the back of the net with a powerful drive from distance, but there was some controversy surrounding the goal.
Indeed, City felt that they should have had a penalty down the other end for a Trent Alexander-Arnold handball; VAR, though, checked the incident and were happy that no offence had taken place.
Raheem Sterling then headed a De Bruyne free kick wide of the post from close range during a frantic period of the match inside a noisy Anfield.
City were playing all of the football and had another opportunity in the 12th minute when De Bruyne delivered a stunning free kick into the Liverpool box, but Aguero could not make contact.
The Reds incredibly doubled their lead in the 13th minute, though, when Salah headed a brilliant Andrew Robertson cross into the bottom corner.
Pep Guardiola's side had been the superior side in the early exchanges, their inability to defend had cost them dearly, though, as the league leaders opened up a two-goal advantage.
Angelino then had one deflected onto the post in the 29th minute after breaking into the Liverpool box, but the left-back continued to find it difficult to contain Salah down the other end.
Roberto Firmino had the chance to send Liverpool 3-0 ahead 10 minutes before the break after finding space just outside the City box, although the Brazil international's effort was always rising over the crossbar.
Bravo then kept out a powerful drive from Firmino as the home side looked to put the match beyond City before the end of the first half at Anfield.
Aguero had two chances for City in the closing stages of the first period, but the Argentina international fired one wide of Alisson's post before finding the gloves of the goalkeeper minutes later.
The visitors were the better team at the start of the second period and had a half-chance in the 49th minute through Ilkay Gundogan, but the midfielder's deflected effort just looped over the Liverpool goal.
The home side effectively put the match beyond their opponents in the 52nd minute, though, when Mane headed a Jordan Henderson cross into the back of the net for 3-0.
Sterling had one deflected high of the crossbar as City attempted to respond, but Liverpool had their three-goal lead in tact heading into the final 30 minutes of action.
Aguero had a golden chance to score in the 67th minute after being found by De Bruyne in a dangerous position, but the South American completely missed the ball.
It just was not to be for the striker on the afternoon, and Gabriel Jesus was introduced shortly after with the Brazilian looking for success where his teammate had failed.
City's afternoon was almost summed up in the 74th minute when they went short from the back and Stones cleared into touch under no pressure, which left Guardiola bemused.
Aymeric Laporte's injury has hurt the champions badly, and it would be a huge surprise if they did not attempt to bring a new central defender to the club during the January transfer window.
The visitors did have one back in the 79th minute when Bernardo Silva picked out the bottom corner from a low Angelino cross, which sparked a late rally at Anfield.
Sterling was the player carrying the fight, and City had another shout for a penalty turned down when Alexander-Arnold appeared to handle once again.
It just was not to be for the Citizens, however, as they suffered a 3-1 defeat to leave them in fourth position in the table, some nine points off the summit heading into a two-week break.
Next up for Liverpool is a trip to Crystal Palace on November 23, while City will attempt to return to winning ways when they host Chelsea on the same afternoon.
LIVERPOOL (4-3-3): Alisson; Trent Alexander-Arnold, Lovren, Van Dijk, Robertson; Fabinho, Wijnaldum, Henderson (Milner 61'); Salah (Gomez 87'), Firmino (Oxlade-Chamberlain 79'), Mane
MANCHESTER CITY (4-3-3): Bravo; Walker, Fernandinho, Stones, Angelino; Gundogan, Rodri, De Bruyne; Bernardo, Aguero (Gabriel Jesus 71'), Sterlingbody check tags ::