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 responded well, with Lolley admirably levelling.
For all of Huddersfield's work to get back in the game a 15-minute blitz by the Hammers at the start of the second term secured all three points in style for the visitors as a goal from Marko Arnautovic and a double by Manuel Lanzini sealed the victory.
Under the Scot, Lanzini and Arnautović have contributed eight goals and nine assists with the latter in particular discovering a rich vein of form since a club-record switch from Stoke City last summer.
Just two passes into the second half, Arnautovic was flicking the ball over the head of Tommy Smith and volleying past Lossl.
Three soon became four as Lanzini and Arnautovic ran riot in the final third, with the Austria worldwide using his pace and power to steam into the box before Lanzini latched onto the leftovers to fire the ball into the roof of the net in the 61st minute.
Mark Noble's opener for the London side in the 25th was cancelled out before the interval by Huddersfield midfielder Joe Lolley.
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The second half blitz was completed five minutes later when Arnautovic broke from the halfway line and found Lanzini who blasted past Lossl from the centre of the area.
On his first start in the PL he cut inside from the right and curled a beauty into the far corner with his left foot. 1-1.
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.
West Ham boss David Moyes (on Arnautovic): "I think he needed to show he can run and he will run and when he does he's a real handful".
"We have a long way to go but the players have done brilliantly well since we came in and they did very well today", he said.
It took this mistake to lift the fixture out from its unproductive period of cat and mouse, and Wagner's team began to play more like a side with home advantage. "Good, I hope he enjoyed us winning".