The Hammers have gone from strength-to-strength under David Moyes, which has seen them move steadily away from the relegation zone and into a mid-table position.
Jonas Lossl's short kick-out put his defence under pressure and Arnautovic was there to hound Lolley out of possession.
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 across had too much pace for his French teammate.
It's not unusual in the Premier League, for example, for players who are not in their club teams to think they can move on when, in fact, they can't. The midfielder received the ball from Aaron Mooy before beating two defenders and curling past Adrian with his left foot.
A long ball from Angelo Ogbonna was flicked onto the Austrian by Cheikhou Kouyate, he lifted it over Tommy Smith and lashed beyond Lossl to restore West Ham's lead.
West Ham were understandably delighted with the result and were equally impressed with the performance from Arnautovic during the game, taking to Twitter to provide their reactions.
Neither the Argentine Lanzini nor Austrian worldwide Arnautovic are out-and-out strikers but with Andy Carroll injured, Moyes paired them up-front and they played like they had been a partnership for years.
Lanzini added insult to injury for Huddersfield as Arnautovic raced free and played in the Argentine playmaker who rifled home his second, and West Ham's fourth, of the game.