The home side's task was made easier by the dismissal of Vanuatan defender Ken Masauvakalo in only the 12th minute of the game.
The Caledonians' midfield maestro Pierre Wajoka was the first to score after 36 minutes, and Michel Hmae added a second goal on the hour mark. Patrick Diaike completed the misery for Vanuatu in the 87th minute.
While Vanuatu are now definitely out of the running, New Caledonia have moved to within a point of group leaders New Zealand, who have a game in hand over the islanders. The home-and-away contest between these top two countries in September will decide the fate of the Oceania group.