After a positive first half had yielded no goals, Adam McGurk took advantage of some unsure goalkeeping to open the scoring.
Jason Shackell headed the second tier side level before substitute Conor Chaplin sent Fratton wild with a cool finish.
Paul Cook rung the changes, with seven players making way from the side that comfortably beat Dagenham in the league at the weekend.
In came McGurk, Jayden Stockley and Brandon Haunstrup for their full debuts, while there were also starts for Paul Jones, Adam Webster, Ben Close and Danny Hollands.
Only Ben Davies, who wore the captain’s armband, Matt Clarke, Gareth Evans and Kyle Bennett retained their places in the line-up.
Pompey were certainly not over-awed against their Championship opponents and immediately looked to get at Derby.
Haunstrup was finding plenty of joy down the left and saw one cross blocked before another just failed to find Stockley.
A ball then fell invitingly to McGurk inside the box, but he dragged his angled drive wide of the post.
Bennett also failed to find the target and was then involved in a neat passing move with Close and Stockley that ended with Alex Pearce heading clear.
It was the Blues looking more threatening without really testing Rams keeper Lee Grant and Bennett saw another couple of long-range efforts fly narrowly wide.
Derby created their first opening in between, with Craig Forsyth finding Andreas Weimann and the Austrian seeing his shot deflected behind by Webster.
Grant was called in to action on 32 minutes and did well to turn behind Haunstrup’s angled strike.
Despite Pompey’s dominance, it was the visitors who had two good opportunities to open the scoring late in the half.
First they got opened up at the back and a well-placed Clarke had to clear Johnny Russell’s low cross from the line.
Jeff Hendrick then did well to burst through the centre and advance on goal, but sent his shot inches past the post.
Derby County 0
It was Derby who were first to threaten after the restart and Weimann had an effort deflected into the side netting.
But it was the Blues who broke the deadlock on 49 minutes, with McGURK netting on his debut.
The goal owed a lot to the work of Stockley, who broke down the right and sent in a teasing cross for his team-mate.
McGurk met it well, but Grant should have done better, with the County stopper only able to help it into the net.
That’s was McGurk’s last meaningful contribution and he soon made way for Enda Stevens.
But that failed to blunt Pompey’s attacking verve and they almost doubled their lead on 56 minutes.
Bennett delivered the ball into the box and first Stockley and then Davies saw efforts well saved by Grant.
Chaplin then came on for Haunstrup as Cook decided to shuffle his pack once more.
However, Derby grabbed an equaliser on 74 minutes when Shackell found space at the far post to head home Russell’s corner.
But they were not level for long and Fratton erupted when Stevens sent in a low cross that CHAPLIN expertly guided past Grant’s grasp and into the net.
The breathless play continued and the visitors felt aggrieved when they were denied a spot-kick moments later.
Hollands appeared to foul Russell inside the box, but referee Paul Tierney felt otherwise and the victim’s free-kick went over.
Derby poured forward in search of an equaliser in the closing stages, but the Blues held firm to book their place in Thursday’s second round draw.
Pompey (4-2-3-1): Jones; Davies (c), Webster, Clarke, Haunstrup (Chaplin 71); Close, Hollands; Evans, Bennett (Tollitt 74), McGurk (Stevens 55); Stockley
Goals: McGurk 49, Chaplin 76
Subs not used: Murphy, Burgess, Atangana, Tubbs
Derby (4-2-3-1): Grant; Ssewankambo (Thorne 70), Pearce, Shackell, Forsyth; Hendrick, Baird (c); Russell, Dawkins (Ince 60), Weimann; Bent (Martin 60)
Goals: Shackell 74
Subs not used: Carson, Keogh, Warnock, Hanson
Referee: Paul Tierney
Attendance: 11,573 (1,134 away fans)