West Ham's opening goal came from a sloppy Huddersfield goal kick; Jonas Lossl's pass to Joe Lolley was intercepted by Arnautovic, before the Austrian fed Hammers skipper Mark Noble who slotted the ball past Lossl's near post.
Huddersfield rallied, however, and David Wagner's team could have equalised when Ince and striker Laurent Depoitre combined, but the chance was wasted when the former's cross had too much pace for his French teammate.
The Terriers eventually got their reward, and it was Lolley - on his first Premier League start - who redeemed himself. The midfielder received the ball from Aaron Mooy before beating two defenders and curling past Adrian with his left foot.
Huddersfield's response ended there, however, as Arnautovic set West Ham going 11 seconds into the second period with a strike from the edge of the area. Cheikhou Kouyate's long ball - the first pass of the half - was headed over Tommy Smith before being rifled past Lossl.
West Ham, now with a stranglehold on the game, went further in front, with Arnautovic the architect this time. The 28-year-old played Lanzini through before the midfielder slotted the visitors' third.
Arnautovic claimed his second assist of the afternoon on the counter-attack, as the Austrian shrugged off the challenge of Schindler before playing in Lanzini for his second goal.
Huddersfield had the chance to grab a consolation as midfielder Alex Pritchard, who was making his debut from the bench after joining from Norwich City, had a free kick saved before Angelo Ogbonna recovered to prevent Depoitre slotting in a rebound.
HUDDERSFIELD TOWN (4-2-3-1): Lossl; Smith (Kongolo, 71), Jorgensen, Schindler, Malone; Hogg, Mooy; Van la Parra, Lolley (Pritchard, 65), Ince; Depoitre
WEST HAM UNITED (3-5-1-1): Adrian; Collins, Ogbonna, Creswell; Zabaleta, Kouyate, Obiang, Noble, Masuaku; Lanzini (Rice, 85); Arnautovic (Ayew, 83)