Arsenal opened up a four-point advantage courtesy of their 3-2 success over Tottenham Hotspur in the North London derby, but Man City ensured that their destiny remains in their own hands in terms of the championship with a routine success at Forest.
Pep Guardiola's side, who are bidding to win the Premier League for the fourth season in a row, remain second in the table but are now just one point behind the Gunners with a game in hand, while Forest stay 17th, one point ahead of 18th-placed Luton Town.
Josko Gvardiol made the breakthrough in the 32nd minute with a header, before Erling Haaland capped his return from injury with a cool finish in the 71st minute.
Man City remain in charge of Premier League title race
There were boos from the Forest fans ahead of kickoff for the Premier League anthem, which was not all that surprising considering their points deduction and the events of last weekend against Everton.
Forest actually had a sight of the Man City goal inside the opening 20 seconds, but Neco Williams could not make proper contact on a dangerous cross into the away side's box, with the champions given a let-off at the City Ground.
Man City came close down the other end in the eighth minute, with Kevin De Bruyne's low strike taking a deflection off Williams before it was pushed wide of the target by Forest goalkeeper Matz Sels.
Williams was heavily involved at both ends, with Ederson having to palm a strike from the defender wide of the post in the 15th minute; Forest's number seven everywhere in the early exchanges before being forced off through injury, and Man City were struggling to gain control of what was a lively contest in Nottingham.
Chris Wood nodded over the crossbar in the 28th minute, but Man City took the lead four minutes later, with Gvardiol heading a corner from De Bruyne into the back of the net from close range.
Man City get the job done against relegation-threatened Forest
Forest should have levelled in the 38th minute through Wood, but the striker somehow failed to make proper contact on a cross from Gonzalo Montiel, with Man City again breathing a sigh of relief, and the Citizens, who also saw Murillo hit the crossbar for the hosts in first-half stoppage time, entered the interval one goal ahead courtesy of Gvardiol's header.
Wood had another big chance early in the second period after excellent work from Anthony Elanga, but the forward saw his close-range effort blocked by Gvardiol.
Julian Alvarez lifted one over the Forest crossbar in the 63rd minute, before De Bruyne's thumping strike was kept out by the home side's goalkeeper four minutes later.
Man City scored a second in the 71st minute, though, with Haaland, who entered the field in the 62nd minute, finding the bottom corner with a composed finish after being found by De Bruyne.
It was always going to be a long way back for Forest after the second went in, and the visitors closed out the contest to pick up a much-needed three points in their race for the title.
What do both teams have left to come this season?
Man City's final four Premier League matches of the campaign are against Wolverhampton Wanderers (H), Fulham (A), Tottenham (A) and West Ham United (H).
Meanwhile, relegation-threatened Forest's final three fixtures are against Sheffield United (A), Chelsea (H) and Burnley (A), with the clash against the Clarets on the final matchday shaping up to be a gigantic affair.