It led to City taking full advantage, and a double either side of half time from Jesus and two late efforts from Leroy Sane led to City moving to the top of the Premier League table.
Both teams began brightly at the Etihad Stadium, but it was City who were creating the early opportunities with Kevin De Bruyne and Fernandinho forcing relatively comfortable saves out of Simon Mignolet.
At the other end, the City back three were struggling to deal with the pace of Mohamed Salah and Mane but on 25 minutes, City went in front when Aguero ran onto a De Bruyne through-ball and tapped into an empty net after rounding Mignolet.
Liverpool offered a positive response and Jurgen Klopp's side should have been level shortly afterwards when Salah ran onto a pass from Mane, only to direct his resulting shot too close to Ederson.
While Liverpool were still imposing themselves on the contest, the visitors were indebted to Mignolet twice in the space of 60 seconds, with the Belgian making two smart stops to deny both Jesus and John Stones.
However, the main talking point of the match came in the 37th minute when Mane was controversially given a red card after catching Ederson in the face with his boot when challenging for a through-ball on the edge of the penalty area.
The incident was open to interpretation due to Mane's focus being on the ball, but his foot made a strong connection with the goalkeeper's face, who then had to be substituted after seven minutes of treatment.
City soon capitalised on having the extra man and six minutes into added-on time, Jesus doubled his team's advantage with a header into the net from eight yards after meeting De Bruyne's inswinging delivery.
Liverpool introduced Alex Oxlade-Chamberlain for his debut at the start of the second half, but the new signing was effectively a passenger as City dominated through until the full-time whistle.
The home team's third goal came through Jesus, who had the simple task of converting into the net from close range after Aguero unselfishly squared the ball to his teammate when bearing down on goal.
Pep Guardiola opted to withdraw Jesus due to his late return from South America, but City continued to control proceedings with De Bruyne blazing over from 12 yards after meeting Sane's cross.
Mignolet had to be alert to prevent Joel Matip from deflecting the ball into his own net but 13 minutes from time, City added to their tally when Sane finished neatly from close range after getting on the end of Benjamin Mendy's delivery.
In the first minute of added-on time, Sane added his second of the afternoon with a stunning fifth, with the German curling the ball into the top corner of the net from 25 yards out.
The scoreline was harsh on Liverpool with Mane's dismissal leading to their defeat, but City took their opportunity after initially finding thing difficult in the opening quarter of the contest.