Our second string's top scorer pounced twice from close range after 12 and 31 minutes before drilling home his third five minutes later.
That made it 14 goals in 15 reserve appearances for the 20-year-old whose displays this season have earned loan spells at Leyton Orient and Northampton Town.
Mounir El Hamdaoui had already opened the scoring after two minutes as we completed the first half 4-0 up.
As is usually the case in these situations, we couldn't quite match that level of performance in the second half and Derby hit back to make it 4-2.
However, Emil Hallfredsson, impressive on the night in a left-back role, made sure we had the final word with the fifth goal in injury time.
There was a determined look about the side from the first whistle with coach Clive Allen no doubt keen to put a couple of indifferent performances behind them.
He started with a 4-3-3 system with Mark Yeates and Johnnie Jackson providing a formidable partnership in central midfield, Emil Hallfredsson bombing forward from left-back and Michael Malcolm pushed forward in right midfield. Up front, El Hamdaoui and Barnard looked sharp as tacks.
El Hamdaoui handed us the perfect start with just two minutes on the clock. The goal owed a lot to Yeates, who picked the ball up deep, travelled 30 yards and slipped the perfect ball for the Moroccan striker to slot home.
Barnard was inches away from David Limbersky's cross before doubling the lead after 12 minutes. Again it came from the right as this time Malcolm's cross was deflected by Jamie Vincent, Miller spilled and Barnard was there for a poacher's goal two yards out.
Derby saw a couple of promising early attacks fall down on the final ball and went close when Lionel Ainsworth drove across Radek Cerny but a yard wide.
Miller made up for his slip for the second goal with a superb full-length save to deny the lively Limbersky after 25 minutes, the Czech youngster connected sweetly after El Hamdaoui rolled the ball square to him 25 yards out.
Confidence was growing by the minute and we didn't have to wait long for the third goal. It was a fine move, Jackson chested down and Yeates volleyed a pass wide to Hallfredsson. The full-back had time to cross and picked out Malcolm at the far post, his header was angled just wide but Barnard was there again to convert from a tight angle, 31 minutes gone.
Barnard completed a 24-minute hat-trick five minutes later. This stemmed from Hallfredsson's break forward, he was held up on the edge of the area but the ball ran out to Barnard who controlled and drilled low into the corner from 25 yards.
Derby struck the woodwork seconds before half-time, Ainsworth darted through and beat Cerny only to see his shot cannon back off the crossbar.
Ainsworth didn't have to wait long to get on the scoresheet though. Only three minutes had passed in the second half when David Cassidy threaded the ball through to the striker in a central position and he finished well from 12 yards.
Yeates almost hit back straight away, shooting low at Miller but Rams had another decent chance after 52 minutes, Giles Barnes dragging his shot wide unopposed from 20 yards.
There was a moment of controversy two minutes later as Miller came out of his area to meet El Hamdaoui only for the striker to get to the ball first. Miller handled but the referee chose to show a yellow card.
He was soon in action again to keep out Limbersky's dipping effort and Barnard was inches away from a fourth after a defence-splitting pass out of defence from Goran Bunjevcevic.
In keeping with the game, the next goal wasn't too far away as the visitors made it 4-2. Cassidy provided the ammunition again, this time a clever pass with the outside of his right foot found Barnes breaking from deep and Barnes finished in style, shooting first time from 20 yards.
The second goal clearly lifted Derby and Ainsworth might have made it 4-3 after 68 minutes but completely missed the ball 10 yards out. He then scuffed one into Cerny's hands from the edge of the box.
As the game became a little scrappy for the first time, Cerny flew to his left to take a routine save from Mitchell Hanson's header and then out of nowhere, Yeates cracked one from 30 yards that clipped the top of the crossbar.
Jackson soon forced the save of the night from Miller, who tipped over his 25-yard screamer and El Hamdaoui somehow skied over Limbersky's cross from six yards.
El Hamdaoui and Barnard both tried their luck before a fifth goal in injury time as Hallfredsson buried Limbersky's low cross.
Spurs: Cerny, Dilevski, Hallfredsson, Jackson, Riley, Bunjevcevic, Limbersky, Yeates, Barnard, El Hamdaoui, Malcolm. Subs: Seanla, Eyre, Price, Kyriacou, Heller.
Derby: Miller, Jackson, Vincent, Turner, Hanson, Martin, Ainsworth, Barnes, Ashton, Cassidy, Holmes. Subs: Booth, Richardson, Davies, Nix, Meredith.
2mins: GOAL. Yeates drove forward before slipping perfect pass to El Hamdaoui, who controlled and slotted past Miller from eight yards.
Spurs 1, Derby 0
12mins: GOAL. Malcolm's cross from the right deflected off Vincent and made it awkward for Miller, he couldn't gather and Barnard was there to mop up fromn close range.
Spurs 2, Derby 0
24mins: SAVE. After good work from Yeates and Barnard, El Hamdaoui ball rolled into path of Limbersky who struck a fierce drive from 25 yards that Miller turned around at full length.
31mins: GOAL. Deep cross from Hallfredsson headed back across Miller by Malcolm at far post, ball was heading just wide but Barnard there again to turn in from tight angle.
Spurs 3, Derby 0
36mins: GOAL. Barnard completes hat-trick. Hallfredsson break from midfield into box, held up 18 yards but ball played wide to Barnard who drilled low into the corner from 25 yards.
Spurs 4, Derby 0
44mins: WOODWORK. Ainsworth darted through and beat Cerny from 12 yards only to see his shot cannon back off the crossbar.
Half-time: Spurs 4, Derby 0
48mins: GOAL. Cassidy threaded ball through to Ainsworth who took his chance well from 12 yards.
Spurs 4, Derby 1
54mins: YELLOW. Controversial moment as Miller came out of his area to meet El Hamdaoui, the striker lifted the ball over him, Miller handled outside his box but referee only showed yellow card.
62mins: GOAL. Another fine pass from Cassidy with the outside of his right foot found Barnes breaking from deep and he buried first time from 20 yards.
Spurs 4, Derby 2
81mins: WOODWORK. Yeates' 30-yarder clipped the top of the woodwork.
Injury time: GOAL. Limbersky crossed low from the right for Hallfredsson to bury from close range.
Spurs 5, Derby 2
Final score: Spurs 5, Derby 2
Lee Barnard scored a 24-minute hat-trick as we toppled Derby County 5-2 in an eventful reserve clash at Stevenage on Wednesday night.