The home side went ahead shortly after half-time through Rudy Gestede's third goal in his last four matches but Derby's on-loan Chelsea star rewarded his side's attacking endeavour with a superb curling shot seven minutes from time.
It means the Rams are now two unbeaten after losing three previously in all competitions, while Rovers have gone two games without a win but showed enough character to suggest they will be well in the play-off mix at the end of the season.
Blackburn boss Gary Bowyer made three changes after the 4-1 defeat to Nottingham Forest as Paul Robinson and Jordan Rhodes returned, while Rams manager Steve McClaren made one change after the victory over Brighton, Jeff Hendrick replacing Will Hughes.
Derby bossed the early possession but were indebted to Lee Grant for keeping the scores level after 10 minutes when he flung himself to his left to tip away Gestede's powerful header.
The league's best away side continued to probe with Simon Dawkins somehow finding his way past two players on the left before his cross found its way to Hendrick who drilled over, while Gestede headed over from close range just before that from a long throw.
And Rovers took the lead in the first minute of the second half when Rhodes clipped in a cross for Gestede, who stooped to head in from close range.
Derby responded positively and should have been level after 62 minutes when Craig Bryson's delicate touch allowed Craig Forsyth to burst into the area but he blazed over with only Robinson to beat.
No team has scored more than Derby in the league this season and Hughes almost added to their tally two minutes later with a wonderful close range lob that had Robinson beaten but hit the crossbar and bounced over.
Rovers were under intense pressure at this stage but Tom Cairney continued to impress and he fired in a low cross that nobody could connect with.
Dawkins gave Rovers right back Adam Henley a stern test all afternoon and he turned him inside out before fizzing a shot into the side netting after 79 minutes.
And the Rams got the goal their play deserved after 83 minutes when Bamford picked the ball up 25 yards out and curled brilliantly past Robinson into the bottom corner.
They fell to sleep a minute later though and Chris Taylor set up Todd Kane on the right whose effort flashed just wide, but Derby almost snatched it in a frenetic finish only for Bamford to fire over.