Birthday boy Slaven Bilic saw his West Ham side pick up their first points of the season thanks to second-half strikes from Pedro Obiang and Andre Ayew.
Bilic was able to call again on the services of Andy Carroll, who made his first start of the season and the England striker was quick to get involved, firing in a low cross to Michail Antonio, who was unable to poke home in the second minute.
Javier Hernandez went close ten minutes later when he smashed the ball onto the the crossbar, but that was the closest that either side would get to opening the scoring before the break.
West Ham continued to dominate after the break when Pedro Obiang’s shot took a huge deflection off Zanka and looped over Jonas Lossl in the Huddersfield goal.
This was the first goal that the Terriers had conceded all season, but a second would come only five minutes later, when substitute Andre Ayew sealed the win for the hosts but poking home after the visitors failed to clear from a corner.
The win sees the Hammers move off the foot of the Premier League table and into 18th place.
West Ham: Hart, Zabaleta, Reid, Collins, Fonte, Cresswell, Louyate, Obiang, Antonio, Chicharito, Carroll
Huddersfield: Lössl; Smith, Zanka, Schindler, Löwe; Kachunga, Billing, Mooy, Ince; Van la Parra, Mounié