Enzo Maresca’s men desperately needed a victory at the City Ground to keep pace with the in-form champions, who have taken 27 points from a possible 30, but lost 3-1.
City had a mountain to climb after finding themselves 2-0 down in the 18th minute following goals from defender Jair Cunha and forward Liam Delap.
The visitors were much improved after the break and Rayan Cherki cut the deficit with an emphatic strike into the roof of the net.
But Delap restored Forest’s two-goal advantage in the 73rd minute, rifling home with his left foot past the outstretched hand of Gianluigi Donnarumma to earn his side breathing room.
Forest manager Oliver Glasner sprinted down the touchline to celebrate with his team, who had not managed to score a single Premier League goal at home before Saturday.
City, who won their first seven league games under new manager Maresca, know that even if they close the gap to Arsenal, it might ultimately all be in vain.
The Etihad club are still waiting to discover their fate after being found guilty of more than 100 breaches of Premier League financial rules — with a huge points deduction one potential punishment.
Earlier, Arsenal made hard work of beating struggling Hull to underline their title credentials on the eve of the international break.
Captain Martin Odegaard finally broke the deadlock for the champions and title favourites in the 72nd minute.
Arsenal, who bossed possession at the Emirates, had a claim for a penalty in the closing minutes of the first half after Kai Havertz had his shirt pulled by Nobel Mendy.
But VAR ruled that the German forward was in an offside position in the build-up.
Frustration mounted as the second half unfolded, but Odegaard came to Arsenal’s rescue, scoring his first goal since early September with a poacher’s finish.
Noni Madueke cut in from the right before unleashing a left-footed shot that Hull goalkeeper Konstantinos Tzolakis spilled and Odegaard fired home from close range.
Arsenal manager Arteta praised his players but wants them to be more clinical after they recorded a third 1-0 win in four league games.
“We can still be much better, and we will improve in many phases, and we will get certain relationships to a different level that will be even more efficient,” he said.
“That’s the next step, to have bigger margins and when we have them, the opportunities, put them away to make sure that we don’t have to hang in there the last few minutes.”
In the early kick-off, Leeds struck in the 79th minute through substitute Noah Okafor to end Tottenham’s three-match winning run.
The major talking point in the first half was a challenge by Leeds defender Jayden Bogle on Spurs winger Mathys Tel, which was reviewed for a potential red card by VAR officials before eventually being cleared.
Tel had to leave the field shortly before half-time.
Spurs boss Roberto De Zerbi, disappointed by his team’s second-half showing, refused to be drawn on the incident, which was not reviewed on the pitchside monitor by referee John Brooks.
“In the first situation of Mathys Tel I didn’t see, I can’t say nothing,” he told TNT Sports after the 1-0 defeat.
He added: “I have big confidence in the referee. Nothing changes if he goes to watch the clip or not. I think there was the VAR and if they didn’t take the right decision, I don’t know, but we have confidence.”
Elsewhere, Jacob Murphy put Newcastle on course for a much-needed win with a spectacular strike in the 80th minute at Craven Cottage but substitute Rodrigo Muniz levelled just three minutes later to earn a 1-1 draw.
Forest’s win against City means Michael Carrick’s Manchester United will kick off against Aston Villa on Sunday in the relegation zone. (AFP)