Anything but a Derby win at the Keepmoat Stadium would have sent the Clarets back to the Premier League, following their win earlier on Good Friday, but goals from George Thorne and Chris Martin in each half prevented that.
Thorne's 25-yarder at the end of the first half was barely deserved, but Derby were stronger after the break before Martin diverted in his 19th league goal of the season 11 minutes from the end.
Victory means the Rams, who were already assured of a play-off place before kick-off, kept their slim automatic promotion hopes alive with an eight-point gap behind Burnley with three games to go.
Burnley got their job done amid a chaotic atmosphere at Blackpool.
Michael Kightly's goal earned the win, which came as Blackpool's fans threw tennis balls onto the field in protest at the current state of their club.
Player-manager Barry Ferguson also had to deal with coach Bob Malcolm and substitute Steven Dobbie having an altercation on the sidelines, as his side slipped closer to the drop zone.
Uwe Rosler's Wigan shrugged off last week's FA Cup semi-final disappointment and moved closer to confirming their place in the top six with a 3-0 win over Reading.
Jordi Gomez - whose spot-kick had given the Latics a shock lead against Arsenal at Wembley last week - lashed home a superb opener on the half-hour as his side cruised to victory over Neil Adkins' out-of-sorts Royals.
Martyn Waghorn added a second for the home side before half-time and Callum McManaman's strike six minutes after the break effectively sealed a win which strengthened Wigan's play-off claims and sent their opponents tumbling out of the top six.
Brighton left it late to edge back above the Royals as Bruno Saltor scored his first goal of the season to salvage a vital point in a 1-1 draw at Huddersfield.
The Terriers, who are still not entirely certain of safety, grabbed a sixth minute lead through an Oliver Norwood free-kick and Norwood almost made it two early in the second half only to be denied by a brilliant Tomasz Kuszczak save.
But Brighton were rewarded for their fighting spirit when Saltor grabbed a rare goal with seven minutes remaining.
Bournemouth's hopes of moving further into play-off contention suffered a shattering blow as they crashed 4-2 at home to 10-man Sheffield Wednesday.
Atdhe Nuhiu put Wednesday in front on 16 minutes and although Marc Pugh levelled matters for the home side on the half-hour, Sam Hutchinson restored the Owls' lead before the break.
Yann Kermorgant headed home an Iain Harte corner on 57 minutes to make it 2-2 and the game seemed to swing in the Cherries' favour when Hutchinson was sent off on 63 minutes for a second bookable offence.
But as the home side poured forward in search of a winner they were twice caught on the break, first Leon Best slamming home the rebound after Mihail Antonio's 86th minute strike had hit the bar, then Best blazing back over the halfway line to set up Chris Maguire to make it 4-2 in injury time.
Blackburn's unlikely top six prospects also faded despite extending their unbeaten run of nine games with a goalless draw at home to rock-bottom Yeovil.
Jason Lowe hit the post early for the home side but Rovers could not make the crucial breakthrough while the point leaves Yeovil rooted to the foot of the table with time running out.
There was similar frustration at Charlton who missed the chance to put breathing space between themselves and the bottom three as they were held to a goalless draw at home to Bolton. Visiting defender Matt Mills had the best chance of the game when his early effort was headed off the line.