Blackburn 0 Portsmouth 1:A solitary strike from Kanu was enough to give Portsmouth their first away victory of the year and consign Blackburn to a second defeat in four days.
Kanu's 25th-minute strike was his third goal of the season, adding to Blackburn's woes after their shock loss to Larissa on Thursday in the first leg of a UEFA Cup first-round tie.
The forward's eventual finish had been preceded 60 seconds earlier by a sensational double save from Brad Friedel to deny the Nigerian.
Stealing in behind the Rovers defence, Kanu met John Utaka's cross with a powerful header from seven yards, only for Friedel to claw the ball off his line.
However, the rebound fell at the feet of Kanu, and looking more certain to score at the second time of asking, his stabbed shot was blocked at point-blank range by the American.
If Rovers thought they had enjoyed a fortuitous, yet fantastic escape, they were made to think again almost instantly.
From the halfway line Sylvain Distin pumped a long ball forward that was nodded down into Kanu's path by Papa Bouba Diop.
At that stage Kanu had more work to do than with his two previous chances combined, but he proceeded to shrug off Christopher Samba, rounded Friedel and then brushed aside Stephen Warnock.
From a tight angle the 31-year-old Samba then drilled a shot in between the left-hand post and Samba, who had recovered his ground.
Blackburn flew out of the blocks at the start of this game, with David Bentley inspirational.
It was the England winger's fourth-minute cross that resulted in Roque Santa Cruz cracking a seven-yard header against the bar.
David James then denied Bentley from a 25-yard free-kick before the latter delivered a piercing cross to the far post that was initially chested down by Morten Gamst Pedersen.
The Norway winger flicked the ball back to Benni McCarthy for a sidefoot volley from 11 yards that flashed past the right-hand post, an opportunity from which the South Africa striker should at least have been on target.
Moments later the all-action Bentley drilled over the bar a 20-yard drive from the corner of the area after being teed up by Santa Cruz who had hustled Hermann Hreidarsson off the ball.
Playing a 4-5-1 formation up until then, Redknapp displayed his tactical nous by switching Sean Davis to a holding role in front of the defence.
That gave the midfield and lone striker Kanu more stability and greater breathing space, to which Blackburn never found an answer.
Portsmouth stifled Rovers for the remainder of the first half, and even after the break they struggled to find a way through.
The visitors could even have had a second but for the outstretched fingertips of Friedel as Samba had headed a goal-kick from James goalwards, and but for the intervention, Kanu would have pounced.
Then Davis should have showed a selfish side as he was left with only Friedel to beat after powering into the area, but opted for a pull back that came to nothing.
Rovers huffed and puffed, but other than a save from James to deny Santa Cruz with a low, curling shot and another Bentley free-kick that was inches wide, they barely threatened.
Instead, it was Pompey who came closest to adding to their tally, only for Friedel to again perform heroics in denying Matt Taylor with his first touch in the 85th minute after he had replaced Niko Kranjcar.