Phil Foden gave City the lead in the seventh minute on Saturday (Sunday AEST) when he fired home from Rodri's lay-off, before Erling Haaland headed in a second in the 15th minute from Matheus Nunes' cross.
Midfielder Rodri was shown a straight red card soon after the restart for squaring up to Morgan Gibbs-White and putting his hands on the throat of the Forest midfielder.
The Spaniard's three-match suspension is set to add to Pep Guardiola's selection problems, with the City boss only able to name eight substitutes - two of them goalkeepers.
But City saw out the closing stages to make it six straight Premier League wins and move five points clear with their main rivals all not in action until Sunday.
In other top-flight matches, Luton fought back to earn a 1-1 draw against 10-man Wolves and pick up a first point in the Premier League.
Wolves had midfielder Jean-Ricner Bellegarde sent off in the 38th minute for kicking out at Luton captain Tom Lockyer after sliding in for a tackle.
Pedro Neto gave the visitors the lead five minutes into the second half after latching onto a long ball.
The Hatters, though, were back on level terms in the 65th minute when Carlton Morris converted a penalty following handball from Joao Gomes.
Luton thought they have scored a late winner through Chiedozie Ogbene, but he was flagged offside.
Crystal Palace and Fulham played out a goalless draw at Selhurst Park.
Raul Jimenez went close for the visitors late in the first half when he forced Sam Johnstone into a good save, while Willian also spurned a great chance late on, but sent his low shot too close to the Eagles' keeper.
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