Goals from Emmanuel Adebayor, Cesc Fabregas and Tomas Rosicky were enough to seal the points, with Kanu's cheeky goal for the visitors being a mere consolation.
The Gunners got off to a perfect start when after just eight minutes Adebayor sent David James the wrong way from the penalty spot after the keeper had hauled down Robin Van Persie.
The early goal opened the game up, with both sides going on the offensive. Manuel Almunia got down well to save from former Gunner Lauren on the half hour.
The Gunners could have gone 2-0 up a minute later had it not been for James diving bravely at the feet of Adebayor to prevent to striker from connecting with Fabregas' cross from the right.
Just seconds later, the Spanish midfielder was also denied by the Pompey keeper after he gathered the midfielder's 25-yard drive at the second attempt.
Fabregas did however put the Gunners further in front on 35 minutes when Rosicky's corner was headed on to the Spaniard by Gilberto. Fabregas, two yards out in a crowded penalty area, turned sharply to fire past James into the bottom left corner of the net.
Just two minutes after the re-start, James was on hand to make a fine save from a close-range Senderos header to stop the Gunners adding another.
That was the Arsenal defender's last contribution however as he was red-carded by referee Mark Halsey after bringing down Kanu on the edge of the Gunners area.
The resultant free-kick was palmed away by Almunia but only as far as Matt Taylor, who shot high over the bar from close range.
Ten-man Arsenal re-affirmed their advantage in sensational fashion in the 59th minute when a free-kick on the Portsmouth by-line was passed short by Fabregas to an unmarked Rosicky on the left edge of the penalty area.
The Czech midfielder hit a low drive through a crowd and past James to make it 3-0.
Pompey's response was swift. They reduced the arrears within a minute. John Utaka sped down the right flank to send over a cross that Kanu somehow back-heeled past Almunia.
Substitute Abou Diaby missed a golden opportunity to put the match well beyond the visitors on 72 minutes when he somehow headed Gael Clichy's cross from the left wide of the goal when from just three yards out.
Almunia showed his athleticism to parry a well hit 25-yard drive from Glen Johnson and got down well ten minutes later to stop Utakas's low shot.
Arsenal captain Kolo Toure received an appreciative hug from his keeper when he threw himself in front of a David Nugent shot to divert the ball away for a corner with just four minutes of normal time left on the clock.
The Gunners kept possession well for the remainder of the game to deservedly claimed all three points.