Kanu, Pedro Mendes and an early own goal by Brynjar Gunarsson meant Reading have now conceded 12 goals in their last four games and a late Kevin Doyle consolation was all they had to celebrate.
Pompey on the other hand rediscovered their early-season verve and they continue to trouble the established order at the top of the Premiership.
The early exchanges set the tone for the majority of the game as Kanu's backheel around Gunarsson allowed Matt Taylor space down the left and the midfielder crossed low to the near post for Gary O'Neil to stab the ball wide.
O'Neil was involved again just two minutes later when his cross from the right targeted Kanu in space 12 yards out.
The Nigerian launched himself at the ball, but failed to make sufficient connection to force Marcus Hahnemann into making a save.
Reading were being totally outrun in the midfield with Steve Sidwell unable to make any impression going forward and instead having to track back to watch the movements of the ever willing Sean Davis.
It was Portsmouth's sheer weight of possession that forced the corner leading to the opening goal.
Mendes' set-piece was swung in at the near post and as Kanu got across Gunarsson to head goalwards the Icelandic defender instead succeeded at deflecting it in with his right arm past a flat-footed Hahnemann.
The goal sparked the Royals into making some headway at the opposite end and Steve Coppell's men went close first through Sidwell and then Doyle.
Portsmouth should have doubled their advantage when Benjani was guilty of arguably the miss of the season so far on 22 minutes.
Kanu ghosted past Ibrahima Sonko on the byline and squared leaving the Zimbabwean the simple task of tapping into an empty net, the former Auxerre man somehow took his eye off the ball and it rolled comically under his feet allowing Reading to clear.
Despite all their dominance a second goal for Pompey continued to remain elusive and when Glen Johnson sliced his clearance James Harper released Bobby Convey in space down the left-hand side.
The American international's cross was hacked clears by Linvoy Primus but only so far as Sidwell who rushed his shot, directing it yards wide.
Portsmouth boss Redknapp was forced into a change at half-time with Primus continuing to suffer a hamstring strain and Noe Pamarot coming on in his place.
It did little in disrupt the balance of play as Benjani, once more, was guilty of missing a great opportunity of putting the game beyond Reading.
As Portsmouth broke from a Reading corner Harper, left as the last line of defence, misjudged a long ball over the top and the Zimbabwean nipped in to steal.
Hahnemann came rushing out leaving Benjani with a straightforward lob, but instead the ball dropped harmlessly wide.
His frustration was soon quelled by the home side finally fashioning a second on 52 minutes.
Taylor's cross was cleared by Ivar Ingimarsson but Sol Campbell sent the ball back in to the penalty area and as Gunarsson stepped up looking for offside, he left Kanu unmarked to head his seventh of the season.
With Reading seemingly heading towards another comprehensive defeat they then threatened the Portsmouth goal through first Seol Ki-Hyeon and then substitute Glen Little.
But it proved fruitless as Pompey ran riot with a third as the ever-involved Taylor's corner was poorly cleared by Doyle and Mendes smashed a volley from just inside the penalty area.
The Portuguese midfielder then nearly made a picture book second for himself when he cut back on his right foot and forced Hahnemann into a dynamic fingertip save to avert further embarrassment for the Royals.
It was left for Doyle though to have the final say as Pompey casually sat back on their healthy lead.
Little's corner was not read by David James and Ingimarsson did well in pulling the ball back for the Irish international to caress into an empty net.