Birthday boy Francesco Baiano kept alive Jim Smith's dream of reaching an FA Cup final for the first time after 30 years in management.
The tie was level at 1-1 when Baiano, 31 on the day, curled a 25yard effort into the top corner on 73 minutes to set Derby on their way to the quarter-finals for the second time in three years.
Then eight minutes from time, he fired home from the edge of the box after good work by Stefano Eranio.
It ended Huddersfield's involvement in the tournament and means Derby manager Smith may yet reach Wembley in the FA Cup after three decades of trying.
For Baiano, last night was the high spot of what has been a disappointing second season in English football. However, he is coming good just at the right time and after having to be separated from Darren Edmondson when the duo clashed midway through the second half, the Italian regained his cool to seal victory for his side.
Chris Beech, who put Huddersfield in front in the first game, repeated the dose after a quarter of an hour, but Derby equalised through Tony Dorigo's free-kick on 34 minutes.
Chances were created and wasted by both sides in a game which had more ups and downs for both teams than a roller-coaster ride before Baiano's brace put the game beyond the Division One side.
But those bare facts do not do this thrilling fifth-round replay justice in a match which entertained spectators but exasperated managers Smith and Peter Jackson.
Both defences were caught out time and again as the two attacks gained the upper hand, and the only mystery was how a mere two goals were scored before half-time.
Nico Vaesen made two fine saves to deny Paulo Wanchope, while Deon Burton could have had four inside the first 40 minutes. As well as hitting the frame of the goal twice, he fired into the side-netting and Vaesen denied him at the near post.
Huddersfield took the lead from a corner after Russell Hoult tipped Ben Thornley's drive over. David Phillips' mishit flag-kick evaded several bodies, and the unmarked Beech had the simplest of tasks to stoop and nod home from three yards.
Dorigo levelled after Kevin Gray was penalised for fouling Burton, a decision which prompted a furious Edmondson to remonstrate with referee Paul Durkin and appear to bump into the Dorset official.
His protests were in vain, and after Baiano touched the ball to Dorigo, the former England international unleashed a fierce 25-yard drive which appeared to clip a Town player as it flashed past a motionless Vaesen and into the bottom corner.
Both bosses managed to instil some defensive discipline into their sides during half-time, and opportunities were much harder to come by after the break.
As the deadlock continued, tempers began to get frayed, and after the flash point involving Baiano and Edmondson, Grant Johnson was booked for a reckless challenge on the marauding Wanchope.
Baiano scored his first goal from the free-kick and when he grabbed his third goal of the season soon after, Huddersfield knew they were on their way out.
Derby County: Hoult, Carbonari, Schnoor, Dorigo, Stimac (Delap 88), Wanchope, Bohinen, Carsley, Eranio, Burton, Baiano. Subs Not Used: Poom, Sturridge, Harper, Hunt. Booked: Bohinen. Goals: Dorigo 34, Baiano 73, 82.
Huddersfield Town: Vaesen, Edmondson, Edwards, Johnson, Dyson, Gray, Beech, Phillips (Baldry 80), Stewart, Allison, Thornley (Facey 77). Subs Not Used: Senior, Beresford, Hessey. Booked: Allison, Edwards, Johnson. Goals: Beech 15.
Referee: P Durkin (Portland).
