Huddersfield had not conceded a goal ahead of the clash, but that run was ended with Pedro Obiang's 72nd-minute deflected strike before Andre Ayew doubled the Hammers' advantage to give Bilic a much-needed present on his 49th birthday.
Athletics events at the stadium meant West Ham started the league season with three consecutive away games - and a trio of defeats piled extra importance on their return to a rain-soaked arena that was hardly homely at times last term.
West Ham toiled for long periods after hitting the woodwork early on through Javier Hernandez, whose withdrawal for Ayew 25 minutes from time brought jeers in Bilic's direction.
But Obiang's hopeful effort looped over Jonas Lossl after diverting wickedly off Mathias Jorgensen and Ayew then justified his introduction with a clinching strike from close range.
After seeing Crystal Palace - without a point and now bottom - sack Frank de Boer earlier in the day, Bilic must feel a sense of relief that his side are finally off the mark.
Starting for the first time since April, Andy Carroll's impact was immediate as he controlled a high ball in the box and fizzed a low delivery across the face of goal, agonisingly out of reach of a sliding Cheikhou Kouyate.
West Ham kept pushing and Hernandez was unfortunate to see a right-footed strike crash off the crossbar after a fine Michail Antonio run on the right.
More good work from Antonio - this time on the opposite flank - then forced a free-kick, but Lossl gratefully gathered as James Collins' deflected header dropped tamely on the goal line following the set-piece.
With Carroll and the looming threat of his aerial prowess continuing to occupy the Huddersfield defence, a half-cleared cross broke for Kouyate to screw horribly wide from inside the area.
Joe Hart was forced into a first save after 54 minutes, dealing well with a long-range Philip Billing effort that skidded across the surface.
Kouyate poked wide at the other end shortly afterwards and it looked as though West Ham's wait for a league win would go on until fortune intervened.
Obiang's left-footed shot from 25 yards looked harmless until it struck the back of the unwitting Jorgensen and looped up and over the goalkeeper via the right-hand post.
The tension lifted and Huddersfield's resolve broken, Ayew profited from a goalmouth scramble after a right-wing corner by prodding into the net.
Back came the visitors as Hart saved low from Steve Mounie and then watched Tom Ince smash against the crossbar, but West Ham held out to claim a huge three points.