Sergio Aguero had opened the scoring for Pep Guardiola's side before Mane was shown a straight red card for a dangerous challenge on home goalkeeper Ederson shortly before the break.
Liverpool had started brightly, with Mohamed Salah providing early threat and a strike from distance by Alberto Moreno deflected wide of the target.
But City soon hit back as Gabriel headed wide from a free kick, before Liverpool failed to capitalise when Salah won a dangerous set piece for the visitors after a crude Nicolas Otamendi challenge.
Kevin De Bruyne forced Simon Mignolet into action with a low shot with an open game still in its first 10 minutes before neat work by David Silva and Otamendi almost gave Gabriel a chance to burst into the box.
As the 15-minute mark approached, Fernandinho fired in a 30-yard effort that Mignolet tipped away, and then Firmino got a touch on a Jordan Henderson ball into the area but Ederson saved.
Trent Alexander-Arnold was booked for fouling De Bruyne on the left but the Belgium international's delivery was easily cleared.
Salah, having a bright game, burst down the right for Liverpool only to send a tame cross straight to the waiting Ederson -- and with 24 minutes gone he was made to pay as De Bruyne played in Aguero, who rounded Mignolet to become the Premier League's all-time leading non-European scorer.
Within moments, Salah was troubling City down the right again and this time produced a better cross which Ederson did well to claim.
After 28 minutes, Emre Can curled an effort well off target after Fernandinho had been booked for bringing down Mane on the edge of the box and, on the half-hour, Ederson made a good stop to deny Salah after he had found space inside the City area.
Gabriel Jesus seized on an error from Ragnar Klavan, who recovered well to block his shot, and then John Stones, forward for the corner, saw his strike loop away off Mignolet's foot.
After 37 minutes Liverpool were down to 10 men when Mane, chasing a ball over the top, clattered into Ederson with a foot raised and was shown a straight red card by referee Jon Moss.
Following a long stoppage, Ederson was stretchered off and replaced by Claudio Bravo as the fourth official indicated eight additional minutes at the end of the first half.
With two of those minutes played, City thought they had doubled their lead when Gabriel headed home -- but the offside flag was up. His frustration was short-lived, however, as superb play by De Bruyne down the right brought a cross that he powered past Mignolet to all but wrap up the points.
Visiting manager Jurgen Klopp made a change at the break, bringing on Alex-Oxlade Chamberlain for Salah, but City grabbed a third after 53 minutes when Fernandinho threaded a fine ball through to Aguero, who unselfishly set up Fernandinho to get his second goal of the afternoon.
Guardiola replaced the striker with Leroy Sane soon afterwards and then Klopp made another change, introducing former City player James Milner for Georginio Wijnaldum.
With the home side coasting on their three-goal lead, Klopp made his final switch, bringing on youngster Dominic Solanke for Firmino, and as the match entered its final 20 minutes City made another change as Otamendi was replaced by Eliaquim Mangala.
Mignolet made a good stop to prevent an own goal when Bernard Mendy's low cross from the left came off Klavan and was heading into the corner before the keeper stuck out an arm to deflect it to safety.
But City did make it four with 13 minutes left as Mendy fired in another dangerous cross and substitute Sane smacked in a first-time finish past Mignolet.
A frustrated Can was booked for a late challenge on Aguero, and there was still time for further damage to be inflicted on Liverpool as Sane curled a sumptuous last-minute strike high beyond the demoralised Mignolet.