Town made an excellent start. Hammers goalkeeper Lukasz Fabianski had to be alert to palm the ball away from the on-rushing Aaron Mooy.
From the resulting corner, Steve Mounie went close with a powerful header which smashed against the crossbar.
But after Terriers stopper Jonas Lossl saved a one-on-one with Marko Arnautovic, home midfielder Alex Pritchard scampered forward and seemed to catch Fabianski out with a low shot which lacked pace but crept inside the post.
It was the first goal a Huddersfield player had scored at home since Tom Ince back in April, last season.
Amazingly, Town hit the woodwork for a second time inside the opening 16 minutes when Philip Billing's cross evaded everyone, hit the inside of the post but rolled away to safety.
The hosts were dominant, but they had to be alert to the counter-attack from West Ham. Felipe Anderson drove down the left flank, only to see Schindler produce a fine block.
Mounie had a glorious chance to make it 2-0, after the visitors were caught in possession at the back, but Fabianski rescued his defenders with a low save down to his left.
Town were forced into a change before half-time, Chris Lowe stretchered off - with what looked a shoulder injury - to be replaced by Erik Durm.
West Ham also made a change at the break, bringing on Chicharito for Grady Diangana to provide more of an attacking threat.
And the former Manchester United striker spurned a great chance to equalise, heading onto the top of the goal with Lossl beaten.
Pritchard fired wide, under pressure from Issa Diop, after breaking clear, while at the other end Pedro Obiang headed Robert Snodgrass's corner across goal, but wide of the far post.