Alex Pritchard looked to have given David Wagner's men a second successive victory when his sixth-minute goal, the first from a Huddersfield player at home since April, established a lead the Terriers held for over an hour.
However, an improved second half from the Hammers eventually ensured they stretched their unbeaten streak to three top-flight fixtures.
Felipe Anderson, a scorer in last weekend's 4-2 win over Burnley, was the hero as he drove home amid a goalmouth scramble.
An eventful opening 45 minutes for Lukasz Fabianski began with an expert early save from Steve Mounie's close-range header.
His reflexes were less impressive for the opener, Pritchard creeping a seemingly innocuous low shot inside the near post.
Philip Billing almost caught out the goalkeeper a second time when his misdirected cross looped against the far upright and back across the face.
The Poland international redeemed himself with another denial of Mounie in a one-on-one, before the Terriers' encouraging half ended with Chris Lowe being taken off on a stretcher after landing awkwardly on his shoulder.
Javier Hernandez's introduction at the interval should have quickly brought about an equaliser, only for the striker to nod over a point-blank rebound from Jonas Lossl's initial save.
It was instead left to Felipe Anderson to drag the visitors level with the Brazilian rifling home following a succession of blocked efforts in the box.
And Manuel Pellegrini's men might count themselves unfortunate not to have pocketed three points in the end, with Socceroos star Aaron Mooy to thank for blocking an Issa Diop header on the line moments after parity was restored.