Coach Matt Parish was only able to name 18 fit players ahead of Monday's victory over Papua New Guinea, and on Tuesday morning Harrison Hansen, Reni Maitua and Frank Winterstein were formally removed from his party.
Tournament officials considered Parish's request to select a replacement and, citing "exceptional circumstances", have allowed new Salford signing Puletua to link up ahead of the final Group B clash with France.
The 34-year-old, who has previously represented New Zealand, played for Samoa in the 2008 World Cup, and could now feature in the quarter-finals, which Samoa all but assured themselves of reaching with their 38-4 win at Hull on Monday.
Australia have not been so fortunate, though, with their request to replace dislocated shoulder victim Luke Lewis turned down.
Lewis suffered the injury when he smashed into an advertising board towards the end of Saturday's win over Fiji.