The Blues had already edged ahead through Sergio Aguero's 24th-minute opener before Mane was dismissed for a dangerous kick that resulted in Ederson being stretchered off.
Gabriel Jesus added a goal either side of the break before a late Leroy Sane brace completed the rout and ensure the Blues' biggest win over the Reds for more than 80 years.
Two teams tipped to challenge for the title, a mixture of heavy showers and sunshine and an open, expansive game to entertain the capacity crowd – this was never going to be a dull encounter.
There were tactical battles all over the pitch as two of Europe’s top coaches tried to keep one step ahead of the other.
Liverpool had the best of the opening few minutes with winger Mohamed Salah a constant threat down the right flank as the visitors looked to expose City whenever Benjamin Mendy and Kyle Walker joined the attack.
Fernandinho’s low drive on 16 minutes was the Blues’ first real effort on target with Simon Mignolet forced to push the ball around the post.
Liverpool continued to prod and probe but City grew into the half with Aguero and Jesus looking increasingly menacing.
It felt like something had to give and on 24 minutes, it finally did.
Kevin De Bruyne collected the ball just inside the Liverpool half before sliding an inch-perfect pass through the Liverpool defence and into Aguero’s path who rounded Mignolet to roll the ball into the empty net.
However, minutes later Liverpool should have been level as Salah raced clear of Nicolas Otamendi and in on goal only to be denied by Ederson from close range.
Johns Stones was then denied from six yards by Mignolet following a goalmouth scramble as the Blues looked to put daylight between themselves and the Reds.
The game’s major turning point came on 37 minutes as Sadio Mane raced through onto a lofted pass from Joel Matip and as the pacy Liverpool forward approached the ball, Ederson bravely headed clear before crashing to the floor courtesy of Mane’s high boot.
Referee Jon Moss took a moment to absorb the incident before issuing a straight red for the Liverpool man for reckless play.
Ederson received treatment for eight minutes before being stretchered off to a standing ovation from all four corners of the Etihad and replaced by Claudio Bravo.
City immediately looked to make their numerical advantage count and the Etihad was on its feet as Walker’s cross was nodded home by Jesus – only for the assistant referee’s flag to deny the Brazilian who’d strayed a yard offside.
Minutes later, Jesus met De Bruyne’s excellent cross and planted his header firmly past Mignolet and this time it did count to deservedly double the Blues’ lead.
Now in complete command, City resumed where they’d left off after the break and were unlucky to see another goal chalked off for offside as Aguero tucked home a low cross, but no matter - just eight minutes after the re-start Liverpool’s by-now wide open defence was breached again.
Stones cut out a Jordan Henderson pass and Fernandinho took over, feeding another slide-rule pass through the middle for Aguero to chase onto, but this time the Argentine squared the ball to Jesus who rolled the ball into the net with Mignolet stranded.
It had been coming and it effectively ended the match as a contest.
The Blues were far from finished.
Leroy Sane added a fourth on 76 minutes after a neat exchange of passes with Mendy ended with the German winger sweeping the ball home from close range .
But the best was yet to come as Sane completed the rout in added time with a superb long-range curling effort to send the home fans on cloud nine and give the Blues their biggest win over Liverpool since 1937 - it's been a long time coming!
Ederson’s bravery not only saved a certain goal but cost Liverpool their in-form striker. It came at a cost for the young Brazilian, too, who must have known he could end up getting hurt.
Terrific stuff from a goalkeeper who looks like he has everything.
City Matchday App star man: Gabriel Jesus
Danilo was drafted into centre defence with Vincent Kompany missing out with a calf problem.
Kyle Walker returned following his one game suspension, while Raheem Sterling served his one match ban.
Team: Ederson, Walker, Stones, Otamendi, Mendy, Danilo, Fernandinho, De Bruyne, Silva (c), Aguero, Jesus
Subs: Bravo, Foden, Mangala, Sane, Gundogan, Delph, Bernardo
City open their Champions League campaign away to Feyenoord on Wednesday evening before travelling to Watford next weekend in the Premier League.