Pompey manager Harry Redknapp has built a well-organised team after a summer of wheeling and dealing, with former West Brom and Arsenal striker Kanu the star capture.
Kanu, who opened the season with a brace in the 3-0 win over Blackburn Rovers, crowned another fine display with two goals at the Riverside Stadium.
The Nigeria international terrorised the Boro defence and, on this form, looks to be one of the signings of the summer.
After a memorable 2-1 win over Premiership champions Chelsea last week Middlesbrough were brought down to earth.
Australia goalkeeper Mark Schwarzer made his 300th league appearance for Boro, but it proved to be a far from happy occasion, although he could not be blamed for any of the goals.
Schwarzer, in fact, denied Portsmouth on several other occasions with brilliant saves.
The visitors took an early lead following a left wing corner by David Thompson, which the Boro defence failed to cut out allowing Kanu to score.
It was an early boost for Pompey, but a disastrous goal to concede from Middlesbrough's point of view.
The home fans obviously hoped their team would bounce back but the Portsmouth defence looked solid.
Middlesbrough had their fair share of the play but Pompey looked more threatening and only a brilliant Schwarzer save at the near post denied Kanu a second.
Gaizka Mendieta went close with a free-kick just before the break as Boro went in search of an equaliser, but the visitors effectively settled the game five minutes after the restart.
Thompson was again the architect, sending over a right-wing cross which Benjani rose high to meet at the far post before planting a header beyond Schwarzer.
Visiting goalkeeper David James then pulled out a magnificent save from Stewart Downing, and even Mendieta joined in the applause.
Pompey further extended their lead in the 57th minute when Kanu raced from inside his own half to beat Schwarzer.
George Boateng chased after the striker but could not risk bringing him down from behind for fear of a red card.
Middlesbrough manager Gareth Southgate tried a bold gamble to pull the game round when he introduced his three substitutes in the 70th minute.
The gamble failed and Portsmouth remained in control, as the home fans began to stream out of the stadium well before the final whistle.
The early leavers missed a fourth goal from the visitors, with Svetoslav Todorov netting in added time.