The Zimbabwean striker celebrated Pompey's 578-minute wait for a home goal in style by running the Rams defence ragged after they had taken a shock early lead through Lewin Nyatanga.
Paul Jewell had recalled the young Welshman from loan at Barnsley and handed him his Premier League debut to the astonishment of many away fans.
Nyatanga though quickly repaid his managers faith by scoring inside the first five minutes after Emanuel Villa's header from a Laurent Robert free-kick hit the crossbar and the Derby defender was on hand to finish.
Kenny Miller could have put them two goals to the good a minute later when he broke through clear on goal but David James spread himself to deny the Scotland international.
Pompey, who were without captain Sol Campbell, were then brought to life through influential midfielder Niko Kranjcar.
The Croatian turned Robbie Savage twice on the edge of the penalty area before lashing an effort just over.
He came even closer five minutes later after Hermann Hreidarsson's cross had only been half cleared with Derby keeper Lewis Price able to smother his low strike.
The respite for Derby was only brief as veteran defender Danny Mills was forced off on 31 minutes leaving Jewell to make a reshuffle at the back.
That seemed to disrupt their organisation and David Nugent and Pedro Mendes combined to lay the ball on for Benjani to turn from close range and grab his tenth of the season.
Four minutes later and Pompey were in the lead as Hreidarsson in unfamiliar waters in the final third of the pitch crossed well for the former Auxerre striker to plant his header past Price.
The second half proved a formality once Pompey had grabbed their third with the goals of the game as Benjani and Mendes counter-attacked with purpose before the striker rolled his finish past Price inside the far post.
Kranjcar and Mendes used the opportunity to showcase some of their extravagant skills with the Derby midfield chasing shadows and yet another defeat leaves them in need of a miracle to stop a speedy return to the Championship.