In a Championship game that the hosts dominated, David Jones and Dean Marney were on target for Burnley, while Derby were reduced to 10 men when Chris Martin was dismissed for two yellow cards at the end of the first half.
Jones gave Burnley the lead in the 29th minute with an audacious lob over former Burnley goalkeeper Lee Grant from the edge of the penalty area, but the game was soured by the dismissal of Martin after referee Robert Madley deemed that he dived inside the penalty area.
Marney tapped home in the 68th minute as Burnley extended their unbeaten league run at Turf Moor to 21 games.
QPR and Nottingham Forest both missed the chance to close the gap on Derby.
QPR were held at home 1-1 by Leeds United, extending their winless run to five games, while Forest lost their first home game since November as Wigan Athletic romped to a 4-1 victory at the City Ground.
Martyn Waghorn, Emmerson Boyce, James McArthur and Jordi Gomez were on the scoresheet for the resurgent Wigan, who move into the top six with the win.
Leaders Leicester City remain eight points clear of Burnley after their 3-0 home win over Charlton Athletic.
Goals were in abundance around the Championship with Bournemouth and Huddersfield Town both finding the net five times at home, while Watford and Bolton Wanderers struck four goals.
Bournemouth inflicted a 5-0 defeat on relegation-threatened Doncaster Rovers with Yann Kermorgant netting a hat-trick, while Huddersfield had five different players on the scoresheet as the Yorkshire club beat local rivals Barnsley by the same scoreline.
Blackpool's winless run is now 16 games after a 4-0 defeat away at Watford, with Troy Deeney and Mathias Ranegie both scoring twice.
Bolton Wanderers eased their relegation fears with a 4-0 win over Lancashire rivals Blackburn Rovers, while Yeovil Town moved off the bottom of the table after a 1-1 draw with Reading.
Yeovil finished the game with eight men after Byron Moore, Joe Ralls and Kieffer Moore were dismissed by referee Scott Mathieson.
A David Lopez penalty saw Brighton and Hove Albion beat Millwall 1-0 at the New Den and Daryl Murphy's ninth goal of the season gave Ipswich Town the same result against Birmingham City.
Sheffield Wednesday's resurgence under Stuart Gray continues after a 1-0 win over Middlesbrough at Hillsborough.
Wednesday have now won six of their last 10 league games and beat Middlesbrough thanks to Atdhe Nuhiu's 87th-minute penalty after Dean Whitehead had been sent off for handling a Leon Best effort on the line.
