Substitute Paul Peschisolido's late strike earned Derby a place in the fifth round of the FA Cup at the expense of Bristol Rovers.
It was an entertaining battle at Pride Park
The Canadian was played in by team-mate Steve Howard and coolly slotted the ball in from just inside the area.
It was harsh on valiant Rovers who saw Richard Walker and Sammy Igoe go agonisingly close with headers.
The game turned in Derby's favour when Aaron Lescott saw red for a foul on Arturo Lupoli with 20 minutes left.
Paul Trollope's outfit did not come to Pride Park to defend and made their intentions clear as early as the third minute when star striker Richard Lambert directed his six-yard header towards goal but into the arms of Stephen Bywater.
Bywater was then forced into acrobatic action, tipping over Walker and Igoe's headed efforts.
When he was beaten by Andy Sandell's header, referee Andy D'Urso came to Derby's rescue by ruling out the goal for a foul on Bywater.
606 DEBATE: Your views on Derby's victory
The Rams' shot-stopper was also forced into clearing a loose goalbound backpass from team-mate Richard Jackson, with the alert Walker breathing down his neck.
The Championship leaders had to increase their forays into Rovers' half, and they did after the break.
Lupoli, their on-loan striker from Arsenal, was unlucky not to score with a header that had to be cleared off the line by Martin Carruthers, while Howard struck his 12-yard effort two feet wide of the Rovers goal.
However, Derby's fortunes changed on 70 minutes when Lescott was shown a straight red for a late tackle on Lupoli.
With the away side down by a man, Billy Davies' men sensed they could steal the win.
And with 10 minutes left they did just that when substitute Peschisolido broke the offside trap to give the home side a valuable yet undeserved win.
Derby boss Billy Davies:
"We knew this cup game would be difficult because we were at home.
"They are 56 places below us but the cup is a leveller. It's a great chance for these teams to come and dig in."
He added: "It was a great goal from 'Pesch'. He's put us in the fifth round for the first time since 1999."
Bristol Rovers boss Paul Trollope:
"We can take a lot of pride from our performance, I said to the boys it was a chance to make their mark.
"In the first half we got hold of the ball and created a lot of chances. I was disappointed we didn't have the lead at half-time."
On Aaron Lescott's red card Trollope added: "A yellow card would have done."
Derby: Bywater, Jackson, Moore, Michael Johnson, Camara, Fagan (Bisgaard 85), Malcolm (Smith 81), Seth Johnson, Barnes, Lupoli (Peschisolido 73), Howard.
Subs Not Used: Edworthy, Oakley.
Goals: Peschisolido 82.
Bristol Rovers: Phillips, Lescott, Hinton, Elliott, Carruthers, Igoe (Rigg 83), Campbell, Disley, Sandell (Haldane 76), Walker (Ryan Green 72), Lambert.
Subs Not Used: Lines, Parrinello.
Sent Off: Lescott (70).
Ref: A D'Urso (Essex).