Jose Reina helped maintain Liverpool's unbeaten start to the season with a smart first-half penalty save to deny Portsmouth's former Arsenal star Kanu.
Reina was at full-stretch to parry away the Nigerian striker's 32nd-minute spot-kick after Benjani had been hauled back by Alvaro Arbeloa.
A combination of Rafa Benitez having one eye on Tuesday night's Champions League clash with FC Porto and losing 18 players to last week's international break, left Liverpool hanging on at the end.
Pompey wasted a host of chances to see off their illustrious opponents with John Utaka and Sulley Muntari particularly guilty of spurning golden opportunities.
Liverpool began the game looking the more likely side to score with Yossi Benayoun going close after a Peter Crouch knock-down inside the first five minutes.Andriy Voronin then wasted the opportunity to play Jermaine Pennant clear by horribly over-hitting his pass.
The flow of the game though was turned on its head on the half-hour mark when Arbeloa was controversially penalised for his foul on Benjani.
The Spanish defender clearly had a handful of the Portsmouth striker's shirt but it was a decision that, in football these days, is seldom given.
However, referee Mike Riley looked over to his assistant before awarding the penalty which Kanu consequently missed.
As Liverpool's jet-lagged legs appeared to tire after the break, Pompey attempted to seize the opportunity to sneak a win.
On 50 minutes Jamie Carragher's defensive header only went as far as Papa Bouba Diop who clumsily fed the ball through to Utaka, but somehow the Nigerian slashed his first-time finish wide.
As the game continued to open up, Voronin turned inside a hesitant Sylvain Distin but his poked half-volley clipped the top of the crossbar.
Muntari then made Utaka's miss look relatively difficult as he scuffed an effort from 12 yards hopelessly over the bar after being set up by Kanu.
Benitez introduced benched Fernando Torres and Steven Gerrard in an attempt to gain an advantage, and within minutes it looked a wise move as the England international midfielder fed the Spanish wonderkid but Torres' miscued shot flew into the stands.
The final 15 minutes bore witness to some frantic football but, apart from Benayoun's attempt to tee up Torres, which was denied by Sol Campbell, the game petered out to a draw.