Goalkeeper Robert Green's last-gasp penalty save denied Portsmouth a place in the top four.
Green dived to his left to keep out Benjani's spot-kick after Danny Gabbidon was harshly adjudged to have handled the ball in the box.
West Ham's Nolberto Solano had earlier been guilty of two horrendous misses, the first of which was a tame header wide from Carlton Cole's cross.
And after Cole's shot hit the bar, Solano headed the rebound wide.
A Hammers breakthrough on either occasion would have been against the run of play.
Portsmouth made an impressive start and Green did well to tip over Niko Kranjcar's dipping 25-yard effort.
606: DEBATE
Pedro Mendes, Kranjcar and Benjani all sent long-range shots wide of the target as Pompey dominated early on.
Kranjcar was a constant threat and his skill opened up the West Ham defence on 35 minutes.
The Croatian collected Hermann Hreidarsson's pass and went past Gabbidon before hurriedly firing wide of the near post with Green bearing down on him.
The visitors barely threatened prior to Solano's first aberration in front of goal.
Solano had been promoted from the bench to the starting line-up along with Luis Boa Morte, with Matthew Etherington a substitute and Lee Bowyer missing out with a knee injury.
Etherington was introduced at half-time in place of Craig Bellamy, who endured a frustrating first 45 minutes and suffered a slight knock.
The change initially made little difference and the home side made an equally determined start to the second period, with Benjani testing Green with a blistering 25-yard drive the England international pushed to safety.
But just as West Ham seemed happy to grind out a point, Solano squandered another simple chance.
And his second miss was even worse than the first.
Cole turned Sol Campbell and after his shot came back off the woodwork, Solano had nobody near him and plenty of time but somehow failed to find the net.
Solano, making his first start for his new club following a recent move from Newcastle, was promply replaced.
It was a full debut the Peruvian will certainly want to forget.
His wastefulness was almost punished by substitute Kanu in the dying minutes.
Kanu, a surprise inclusion on the Pompey bench after a knee injury, let fly with a shot that flew wide of Green's left-hand post.
Green then came to his team's rescue with a fine stop after referee Mike Dean's decision to award a penalty left West Ham incensed.
Portsmouth manager Harry Redknapp:
"I thought it was a penalty. It was harsh, but if you look at Gabbidon he was just inside the box.
"They had the best two clear-cut chances but in the main, we were the dominant team. West Ham didn't deserve to lose though."
West Ham boss Alan Curbishley:
"It would have been an injustice if Portsmouth had taken the points. The handball wasn't deliberate.
"Robert Green showed everyone what he has been like for us this season. That's what he can do."
Portsmouth: James, Johnson, Campbell, Distin, Hreidarsson, Utaka (Kanu 77), Diop, Pedro Mendes, Muntari, Kranjcar, Mwaruwari.
Subs Not Used: Ashdown, Lauren, Taylor, Pamarot.
Booked: Hreidarsson, Diop.
West Ham: Green, Neill, Gabbidon, Upson, McCartney, Solano (Spector 78), Noble, Mullins, Boa Morte, Bellamy (Etherington 46), Cole (Ferdinand 90).
Subs Not Used: Wright, Camara.
Booked: Bellamy, Noble, Solano, Cole.
Att: 20,525
Ref: Mike Dean (Wirral).
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