The match began in emotional fashion as Forest honoured club legend John Robertson with a minute of applause. The hosts, wearing black armbands, started brightly and almost took an early lead when Callum Hudson-Odoi delivered a dangerous cross towards Morgan Gibbs-White, but the midfielder could not apply the finish.
Forest stayed compact and disciplined in the first half, frustrating City and limiting their usual attacking rhythm. Despite City having scored before the break in each of their previous seven competitive matches, neither side managed a shot on target in a tight opening 45 minutes.
City raised the tempo immediately after the restart and took the lead inside three minutes. Cherki slipped a clever pass into the path of Tijjani Reijnders, and the midfielder timed his run perfectly before calmly finishing past John Victor.
Moments later, Cherki nearly doubled the advantage but was denied by Victor at his near post.
Forest responded well to the setback and showed patience and belief. Hudson-Odoi and Gibbs-White combined neatly in the build-up before Igor Jesus pulled the ball back for Omari Hutchinson, who swept a first-time finish into the net to score his first goal for the club and lift the home crowd.
Just as Forest looked capable of holding on, City found a late winner. A deep corner was headed back into the danger area, and Cherki showed composure and quality to drive a low shot through Gibbs-White's legs and beyond the unsighted Victor.
The win made it eight consecutive victories in all competitions for City and extended Pep Guardiola's unbeaten Premier League run against Sean Dyche to 17 matches. The result lifted City to the top of the table for now, while Forest remained just one place above the relegation zone after a spirited display.