Thursday's match was Vanuatu's first of the tournament while Hungary had already had a victory over Greece.
The extra time on the field showed early on with the Hungarians taking a 12-0 lead before the Melanesian side gained some rhythm and found themselves in front late in the game.
However Hungary scored last, eventually winning 18-13.
Vanuatu plays Greece in their last pool match on Sunday.
In Thursday's other game, Niue defeated Malta 26-16 and will now play the Philippines on Sunday with the hope of making the cup semis.