A first-half Robbie Savage penalty and a second-half strike from Paul Green secured another three points for the resurgent Rams, who are riding on the crest of a wave after a shaky start to the season.
Rams skipper Savage slotted home from the spot after Aaron Mokoena upended Tomasz Cywka and Green added a second after the break to end Pompey's run of four consecutive wins in front of the biggest crowd of the season at Pride Park.
Derby were clearly brimming with confidence on the back their impressive form of late and they immediately starting to ask questions of the Pompey defence.
Green burst forward from midfield after 11 minutes and the Republic of Ireland midfielder got to the byline and cut the ball back for the onrushing Kris Commons, whose right foot effort from eight yards out forced Jamie Ashdown to make an outstanding reflex save.
Steve Cotterill's side responded and Dave Kitson's strike was tipped around the post by on-loan Rams goalkeeper Frank Fielding, although referee Colin Webster gave a goal-kick.
But it was Derby who deservedly took the lead 22 minutes in, when the lively Cywka raced into the penalty area and was brought down by Pompey skipper Mokoena.
Webster failed to spot the offence but after consulting with his linesman, he pointed to the spot and Savage held his nerve to send Ashdown the wrong way from 12 yards.
Shefki Kuqi, James Bailey and Cywka had chances to extend Derby's lead before the break but all three failed to hit the target.
But the second goal came 12 minutes into the second half when Green laid the ball off to Cywka and the Polish forward got to the byline and returned the ball for Green, who made no mistake with a simple close-range finish.
Kuqi could have added a third when he met Cywka's inviting corner from the left but the big striker was unable to hit the target with his header.
Pompey boss Cotterill brought on Kanu in a bid to salvage something from the game and the former Arsenal striker could have pulled a goal back 10 minutes from time but fired high and wide.
There was more good news for Derby fans when Miles Addison made a late substitute appearance after a lengthy spell on the sidelines with a foot injury.
And there was almost a candidate for goal of the season from the impressive Commons, when Ashdown cleared straight to the former Nottingham Forest forward and the Pompey keeper had to scramble back to keep out his long-range effort.
Carl Dickinson almost set up a tense finale but the full-back drove over the bar from the angle as Derby stretched their impressive run to just one defeat in nine Championship games.