Portsmouth, who narrowly escaped relegation last season, moved up to second place in the Premier League after a 4-0 win at Middlesbrough on Monday.
Two goals from Kanu and strikes by Benjani Mwaruwari and substitute Svetoslav Todorov put Portsmouth on seven points from three games, two behind early leaders Manchester United.
Kanu struck early to put Portsmouth ahead after seven minutes when he fired home from close range following a corner that eventually found its way to the Nigerian international.
Benjani put the visitors 2-0 in front with a downward header at the far post following a short corner five minutes after the break to score his second goal for the club.
Kanu added Portsmouth's third with a fine individual goal after running from inside his own half before lifting the ball over stranded Boro goalkeeper Mark Schwarzer.
Todorov wrapped up the victory in added time with Pompey's fourth goal after being played in by Sean Davis and lobbing Schwarzer to round off a fine night for the south coast side.
"It was a good performance. We did ever so well tonight," Portsmouth manager Harry Redknapp told Sky Sports.
Middlesbrough, who beat champions Chelsea in their last match at the Riverside on Wednesday, are 16th with three points from three matches under new manager Gareth Southgate.