On a day that saw table-toppers Leicester City held at Blackburn and the second-placed Burnley win at Charlton Athletic, Derby kept clear in third with their victory.
Scotland international Craig Bryson was the star of the show, showing quick reflexes to give Steve McClaren's side the lead in the sixth minute.
He doubled their lead in the 32nd minute and Jeff Hendrick also scored before half-time.
Substitute Johnny Russell hit a stunning long-range effort for Derby's fourth and there was still time for Bryson to complete his hat-trick, netting a 69th-minute penalty to cap a miserable day for Forest's ex-Derby boss Billy Davies.
Leicester's lead was slashed to five points as Blackburn Rovers came from behind to claim a 1-1 draw at Ewood Park.
Matthew Kilgallon's 43rd-minute goal cancelled out Jamie Vardy's early strike.
Burnley kept their title dreams alive with a 3-0 win at relegation-threatened Charlton Athletic, as Ashley Barnes, Sam Vokes and Michael Kightly all netted.
The gap of 10 points between Burnley and Derby means that the automatic promotion places are almost sealed, but the play-off battle continued to heat up as QPR, Wigan Athletic and Reading all won, meaning Forest dropped to seventh.
Ravel Morrison and Bobby Zamora scored in stoppage time as QPR won 3-1 at Middlesbrough, a result that sees them just below Derby on goal difference.
Jean Beausejour and Martyn Waghorn netted as Wigan came from behind to beat Watford 2-1 and Reading climbed to sixth with a win at Birmingham City by the same scoreline.
At the other end of the table, rock-bottom Barnsley's woes continued as Steve Cook's stoppage-time effort helped Bournemouth to a 1-0 win at Oakwell.
Yeovil Town, who sit 23rd, conceded a two-goal lead to draw 2-2 against Bolton Wanderers and Millwall remained in the relegation zone after losing 2-1 at Leeds United.
Ross McCormack – the Championship's top scorer with 25 – netted again as Leeds ended a six-match winless streak.
Other results saw Blackpool win for just the second time since November as they edged Huddersfield Town 1-0 while Doncaster Rovers beat Sheffield Wednesday by the same scoreline in a South Yorkshire derby.
Ipswich Town won 2-0 at Brighton and Hove Albion thanks to second-half goals from Tommy Smith and Daryl Murphy.
