Slaven Bilic's side piled more misery on the Sky Bet Championship's bottom side by coming from behind twice before finishing the job with two goals in five minutes of the second half.
The Baggies maintained their unbeaten start to the campaign and moved up into fourth place in the process having given new Huddersfield boss Danny Cowley plenty more to think about.
Terriers can't buy a win
Huddersfield, who started the match on the back of an 18-match winless run in all competitions, led 2-1 at the break.
Lewis O'Brien gave the Terriers a 16th-minute lead which was cancelled out by Matt Phillips three minutes later, while Karlan Grant restored their narrow advantage 10 minutes before the interval.
On-loan West Ham winger Diangana crossed for Darrell Furlong to head home to make it 2-2 after 70 minutes.
His mazy solo run teed up Phillips to complete his brace and edge the hosts in front before Semi Ajayi grabbed a fourth at the death.
Huddersfield strike first
Huddersfield took the lead with their first attack. O'Brien raced from the centre circle and exchanged passes with Fraizer Campbell before rifling a low left-footed drive past goalkeeper Sam Johnstone into the far bottom corner.
The Terriers' lead did not last long as the home side drew level.
Phillips stroked a sidefooted effort in off the post after Austin - with his back to goal - had helped Furlong's short ball to him 15 yards out.
Huddersfield regained the lead after some awful defending from the hosts. Kyle Bartley's pass from Johnstone was intercepted by Trevoh Chalobah and Elias Kachunga exchanged passes with him before finding Grant, who poked past the goalkeeper from six yards for his sixth goal of the season.
Phillips unleashed an angled drive which Grabara tipped wide before West Brom equalised from the resulting corner.
Phillips passed short to Diangana, who crossed for Furlong to send a powerful, downward header in off the post for his first league goal in almost three years.
Diangana turned provider again as the Baggies took the lead, beating three players before crossing the ball in for Phillips to sidefoot under the diving Grabara.
The unmarked Ajayi sealed the three points late on with a far-post header from Matheus Pereira's corner.
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