Green pulled off a dramatic stoppage-time penalty save from Benjani to deny high-flying Pompey a club record fifth successive Premier League win.
The former Norwich stopper had already produced a series of fine saves to stake his claim for a starting place in England's crucial Euro 2008 decider against Croatia next month.
At the other end Nolberto Solano served up two contenders for miss of the season as the Peruvian endured a nightmare full West Ham debut.
Niko Kranjcar gave the visiting fans an early fright when he drilled a 20-yard left-foot shot just wide of Green's left post with only 31 seconds on the clock.
Green gave Steve McClaren a timely reminder of his ability with a stunning one-handed save to tip Kranjcar's 25-yard blockbuster over the crossbar.
Green came to the Hammers' rescue two minutes later when he spared Danny Gabbidon from an embarrassing own goal.
Herman Hreidarsson came bombing down the left before sending in a teasing low cross which was deflected goalwards off Gabbidon's right heel before Green saved with the legs.
Solano should have grabbed himself a goal against the run of play midway through the first half when he raced onto Carlton Cole's centre.
The Peruvian mis-timed his jump at the back post and failed to make decent contact with an attempted diving header with Pompey's goal gaping.
Worse was to follow as Solano left Curbishley with his head in his hands early in the second half.
Cole smashed a close-range shot against the underside of the crossbar and Solano nodded the rebound wide from two yards after being left with an empty net.
Pompey thought they had won the match in the 93rd minute when Gabbidon needlessly handled inside the penalty area but Green flew to his left to keep out Benjani's spot-kick.