Mark Noble pounced on a lazy pass from goalkeeper Jonas Lossl to put the visitors in front before Joe Lolley equalised with a superb curling effort for Huddersfield.
Marko Arnautovic scored within seconds of the restart and later assisted Manuel Lanzini twice as the visitors ran away with it in the second half.
It was just the fourth time this season that Huddersfield have lost at home.
Victory moves the Hammers five points away from the drop zone and they overtake Huddersfield in the process.
This result means Hammers boss David Moyes becomes just the fourth manager to win 200 Premier League matches, after Sir Alex Ferguson (528), Arsene Wenger (468) and Harry Redknapp (236).
Huddersfield remain four points off the relegation zone but they have a tough fixture against Stoke at the Bet 365 Stadium to follow before hosting Jurgen Klopp’s Liverpool at the end of January.
Arnautovic was forced to miss the 1-1 draw with Tottenham on 4 January but was straight back into the starting line-up at John Smith’s Stadium.
Moyes knew he needed his best players on the pitch and Arnautovic didn’t let him down – picking up two assists and a goal on his return.
He terrorised Huddersfield’s defence all afternoon and despite not making much impact in the first half, there were signs he would become a danger.
His link-up play with Lanzini was on show in the opening stages as the pair created space for each other out wide and constantly switched positions throughout.
The dynamism and creative flair ultimately opened things up but it was Arnautovic’s determination off the ball that got the early second-half goal to regain his side’s lead.
He then weaved in and out of defenders to create Lanzini’s first before the pair linked up again to make it 4-1 and seal three points.
Arnautovic said his team were “on fire in the second-half” but it was his partnership with Lanzini that earned the three points.
