It appears they and opponents West Ham could be heading in opposite directions with the east Londoners leapfrogging them in the table after extending Huddersfield's run without a home win to four games.
Huddersfield were not level for long, though, as Arnautovic stunned the home crowd with his sixth of the season, a powerful drive beyond Jonas Lossl.
Manuel Lanzini scored twice to add to Marko Arnautovic's fierce drive 11 seconds into the second half as the Terriers succumbed to a heavy loss to David Moyes' side.
The second half couldn't have started any worse for Huddersfield.
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.
More news: There is much to learn from the ANC, says KenyattaWest Ham, now with a stranglehold on the game, went further in front, with Arnautovic the architect this time. And to put an exclamation point on a banner second half day, Arnautovic and Lanzini connected once again for the Argentine's brace just five minutes later in the 61st.
The Austria global created the opener for Mark Noble midway through the first half, only for Joe Lolley to level things up with his first league goal of the campaign.
Depoitre headed over another Van La Parra cross and West Ham forward Lanzini shot tamely at Lossl following a swift counter, but the Argentinian made no mistake soon after.
The former Everton and Manchester United manager explained that starting the two together, rather than choosing one and a recognised striker alongside, was a deliberate decision.
- Huddersfield have conceded seven goals in their last two Premier League games, this after conceding six across their previous six. Moyes will hope the joy continues next Saturday against Bournemouth. Anybody who plays well for me, that's why I'm trying to get more than 200 wins, because you can only pick the players you think are going to get the results.
The half-time break ultimately came at the wrong time for Huddersfield who looked reinvigorated by their opener, but any optimism for the second period quickly vanished merely 11 seconds after the referees whistle.
