The Nigerian striker netted the game's only goal with a neat solo strike midway through the first half.
Rovers, who were one of only three teams in the top-flight yet to taste defeat, have now gone three games without scoring a goal.
Before the game, both sides made one change from their last outings. Chris Samba returned from the head injury he sustained against Chelsea in place of Rovers captain Ryan Nelsen, who limped out of Thursday's UEFA Cup defeat away to Larissa FC, whilst Croatian midfielder Niko Kranjcar was preferred to Benjani Mwaruwari for the visitors.
In decidedly defiant mood following the shock 2-0 defeat to the Greek minnows in midweek, Rovers started the game at a canter.
After four minutes, Roque Santa Cruz broke from midfield, before feeding the ball right to David Bentley, who delivered a pinpoint cross which the Paraguayan striker headed against the stanchion. From the ensuing scramble, Morten Gamst Pedersen believed he should have been awarded a penalty, before a free-kick on the edge of the box was given, which the Norwegian took and saw saved.
On ten minutes, Bentley's deep cross to Pedersen was expertly controlled and played inside to Benni McCarthy, who uncharacteristically blazed over the bar, as did Bentley just two minutes later.
Against the run of play, Portsmouth almost broke the deadlock with their first real attack of the game. On 23 minutes, John Utaka crossed from right, Kanu beat the Rovers offside trap, but his free header and then follow-up forced goalkeeper Brad Friedel into a sensational double save.
A minute later, however, and the visitors did take the lead. Papa Bouba Diop headed a long ball upfield into the path of Kanu, who rounded Friedel, held off the challenge of Stephen Warnock and slotted past Samba on the line.
Route one football appeared to be the order of the day for the visitors. Five minutes after the break, a huge goal-kick from keeper David James caused confusion between Samba and Friedel and Kanu was almost gifted his second goal of the game.
Rovers' biggest threat looked to be from set-pieces. Samba failed to control Pedersen's corner at the back post and then the giant Congolese defender couldn't connect with Bentley's free-kick when unmarked in front of goal.
Benjani came on for the visitors and almost set up Portsmouth's second, but somehow Bouba Diop missed the open goal, whilst at the other end, fellow substitute Jason Roberts failed to find a way past James, as Rovers slipped to back-to-back defeats.