Pressure has been mounting on the winless Trotters and boss Dougie Freedman after a woeful start to their campaign that had seen them collect two points from six matches before Tuesday night, yet they made an ideal start against County as Alex Baptiste gave them an early lead.
But in a pulsating first-half Derby, who were aiming for fourth straight away victory at the Reebok Stadium, turned the game on its head through a Johnny Russell double before Chris Eagles levelled proceedings just before half-time.
Bolton dominated for large spells of the second half and while substitute David Ngog wasted their best chance when he put a free header wide, the hosts were earlier grateful for Matt Mills' goal-line clearance from Adam Smith's shot.
While a point ended a run of four straight defeats it was not enough for the home side, who were among the pre-season favourites for promotion, to slip to the bottom of the standings after Millwall's win over Blackpool.
Freedman made three changes to the line-up that suffered a 1-0 defeat against Leeds at the weekend, with defender David Wheatley, midfielder Rob Hall and striker Jermaine Beckford replacing Zat Knight, Darren Pratley and Ngog, all of whom dropped to the bench.
The beleaguered hosts came out with a point to prove against an unchanged Derby side, with Chung-Yong Lee controlling marvellously before teeing up full-back Baptiste, who cut in from the right and stroked home from the edge of the area in the fifth minute.
It was a dream start for Freedman's men, but their lead would last a meagre two minutes as Craig Bryson squared the ball on the left for Russell to tap past Wanderers goalkeeper Adam Bogdan, who perhaps should have done better.
Bolton's luck then went from bad to worse as Bryson and Russell linked up once again to put Derby ahead in the 18th minute.
Will Hughes' tame shot was fortuitously deflected into the path of Bryson, who cut the ball across the centre of the area to leave Russell with a simple finish although the last touch may have come from a Bolton defender.
Stung into action, Burnley almost levelled once more but visiting goalkeeper Lee Grant parried away Eagles' first effort and then made another decent save from the midfielder shortly after, while at the other end Bogdan again showed his vulnerability when he gathered Jamie Ward's free-kick at the second attempt.
But Eagles continued to cause havoc in the Derby backline and he was duly rewarded four minutes before half-time.
There appeared to be little danger when Eagles collected the ball in acres of space 25 yards from goal but the former Burnley man turned quickly and rifled low into Grant's far corner.
A slow start to the second half was punctuated when Mills denied Smith a certain third goal for Derby with a goal-line clearance after Bogdan had only clawed away Ward's cross.
Soon after Bolton striker Beckford managed to weave his way into the box after some fine solo work but sliced wide, while Marc Tierney's teasing cross from the left was smartly headed out by Derby full-back Craig Forsyth.
The home side continued to pile on the pressure, with substitute Ngog providing a useful foil for Beckford, who had been largely anonymous in the first half.
But the Liverpool striker should have done better than glance a header wide after being left unmarked from Smith's ball into the area.