Huddersfield Town ended Manchester United's unbeaten start to the season as Jose Mourinho's side fell five points behind league leaders Manchester City at the John Smith's Stadium.
Everton have now moved five points clear of the relegation zone with a game in hand on Luton Town but Forest remain deep in trouble, only a point ahead of the Hatters.
The win leaves City level on points with Liverpool, who play Sheffield United at Anfield on Thursday night, and a point behind Arsenal, who top the table after beating Luton Town.
Kevin de Bruyne made his return to competitive football for the first time since August as Manchester City began their defence of the FA Cup with a comfortable victory against Huddersfield Town at Etihad Stadium.