All Whites goalkeeper Mark Paston also saved a 51st-minute penalty from Bahrain's Sayed Adnan.
Slovakia's best chance of a breakthrough, though, came through New Zealand's nervy keeper Mark Paston.
Unsurprisingly, only two of his four long-range efforts caused small concern for Paston.
Elvis Lee, 34, kicked and bit Tyler Whelan, who died in hospital after collapsing at his home in Sheepwalk, Paston, near Peterborough.
For historians, the Paston Letters have long been a fascinating insight into the soap opera lives of gentry in the Middle Ages.
Tyler Whelan died in hospital on 7 March 2011, after collapsing at home at Paston in Peterborough, Cambridge Crown Court has heard.
Paston partly redeemed himself with a smart tip-over from Hamsik's long-range effort shortly before half-time, but within five minutes of the restart, he was beaten.
Fallon did strike just before the break but the visitors were handed a route back into the tie when Tony Lochhead fouled Abdulla Omar in the box although Paston stopped Adnan's weak effort.
The holders nearly hit back instantly but All Whites goalkeeper Mark Paston clawed out a dangerously bouncing Riccardo Montolivo free-kick with a posse of blue shirts waiting at close quarters to pounce on any mistake.
The centres under threat are Crofts Corner in Bretton, the Tunnel in Orton Malborne, Charteris in Welland, Chestnuts in Eastfield, the Spinney in Ravensthorpe, Thistle Drive in Stanground and the Peterborough Adventure Playcentre in Paston.
Shots on target could be counted one hand and the best of those came in the second half with Manchester City forward Roque Santa Cruz stinging the hands of All Whites keeper Mark Paston with a 25-yard free-kick.
With play really opening up - as many matches have in the second round of group matches following cagey encounters in the first - Montolivo once more showcased his long-range abilities but again Paston proved equal to his shot by palming it away from danger as the pressure mounted.
The final opportunity fell to Italy as Argentine-born Camoranesi forced another decent stop from Paston - but destiny was on New Zealand's side and, on the balance of chances if not ther amount of possession, they fully deserved to take their World Cup points tally to two following their opening draw with Slovakia.
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