City went ahead in the lunchtime kick-off in the 25th minute through Sergio Aguero before Mane clattered into goalkeeper Ederson with a high challenge at the edge of the penalty area.
Referee Jon Moss brandished the red card to the Liverpool forward, with Ederson taken off on a stretcher and replaced by Claudio Bravo.
The Brazilian tapped in the third goal in the 53rd minute after being set up by Aguero, before substitute Leroy Sane added a fourth from close range in the 77th minute and then curled a superb 20-yard effort into the top-left corner during stoppage time.
Manchester United remain top of the table, above City on goal difference, despite two goals from Cameroon forward Eric Maxim Choupo-Moting to earn Stoke a 2-2 draw in the late kick-off at the bet365 Stadium.
United, though, were back on level terms just three minutes later through Marcus Rashford, who inadvertently deflected a header from Paul Pogba into the net following a corner.
Romelu Lukaku gave United, who had made a 100 per cent start to the new Premier League season, the lead on 57 minutes after his initial shot had been saved by Jack Butland.
Choupo-Moting, though, secured a point for the home side with a header just after the hour, although Lukaku shot over late on and Butland produced a fine reaction stop in added time.
Earlier, Arsenal had eased the pressure on manager Arsene Wenger with a 3-0 win at the Emirates Stadium over Bournemouth, who suffered a fourth straight Premier League defeat.
Danny Welbeck bundled the Gunners ahead after six minutes before club-record signing Alexandre Lacazette doubled the lead after 27 minutes.
Five minutes into the second half, England forward Welbeck slotted a low shot into the far corner as Arsenal bounced back from their 4-0 drubbing at Liverpool before the international break, with Alexis Sanchez, who looked to be leaving ahead of the transfer deadline, coming on for the closing stages.
The German, signed from Ingolstadt in the summer, added a second on 48 minutes before turning provider for Tomer Hemed to head in a third just after the hour.