After Huddersfield had gone in front with a goal by Chris Beech, Derby drew level before the interval through Tony Dorigo. Francesco Baiano, one of Smith's myriad foreigners, marked his 31st birthday with the two second-half goals which guaranteed the Premiership club a place in the last eight.
The match began at a breathless tempo, as if both sides were intent on forcing the other into submission before half-time. With 10 minutes played, the score might have been 5-3 to Derby, who set the tone when Paulo Wanchope set up Deon Burton inside 60 seconds.
The Jamaican's shot shook the post, but Huddersfield signalled their enterprising intentions in their first attack. Ben Thornley's long ball sent Marcus Stewart through against Russell Hoult, only for the striker to pull his drive wide.
The relentless pace continued unabated. At one end, Wanchope forced Nico Vaesen to save with his legs and sent a header over, while Dorigo also brought Huddersfield's Belgian goalkeeper into action. At the other, Hoult tipped Rob Edwards' goal-bound effort behind before Allison wasted an even better aerial opportunity than had Wanchope.
The only surprise was that it took 15 minutes for the breakthrough to arrive. An acrobatic save by Hoult, after Thornley's shot deflected off Igor Stimac, brought Huddersfield another corner. David Phillips swung the ball in low to the near post where Beech, a recent pounds 65,000 recruit from Hartlepool United, stooped to head in.
Derby pushed Huddersfield on to deep and massed defence, producing an equaliser after 33 minutes. Dorigo, having had a free-kick rolled into his path by Baiano, drilled a low shot from 25 yards through the dispersing defensive wall. The ball sneaked into the net between Vaesen and his left- hand upright.
Either side of the goal, Lars Bohinen and Burton rattled the woodwork, although Stimac came within centimetres of conceding a penalty when he barged Stewart over on the edge of the box.
Even so, the contest was remarkable for its lack of stoppages. After a reckless challenge by Rob Edwards on Baiano, Derby's pressure was such that the referee, Paul Durkin, waited nearly 90 seconds for the lull in proceedings that would enable him to flourish a yellow card.
A theatrical dive by Wanchope following legitimate shoulder contact with a defender might have provoked the same punishment. Mr Durkin took no action, however, and again erred on the side of leniency when Baiano and Darren Edmondson scuffled over a ball that had gone for a throw-in.
There was no such escape for Grant Johnson when he brought down Wanchope in the 72nd minute. The Scot's indiscretion proved doubly costly, Baiano lofting the subsequent free-kick into the spot beneath the angle of post and bar from 22 yards.
Baiano put the seal on Derby's success when he took a pass from Burton and beat Vaesen with a low shot from just inside the area. Arsenal will not, one suspects, be nearly so accommodating.
Derby County (3-4-1-2): Hoult; Stimac (Delap, 87), Carbonari, Schnoor; Eranio, Bohinen, Carsley, Dorigo; Baiano; Burton, Wanchope. Substitutes not used: Sturridge, Harper, Hemp, Poom (gk).
Huddersfield Town (3-1-4-2): Vaesen; Edmondson, Dyson, Gray; Johnson; Phillips (Baldry, 79), Beech, Thornley (Facey, 76), Edwards; Allison, Stewart. Substitutes not used: Beresford, Hessey, Senior (gk).
Referee: P Durkin (Dorset).Reuse content