Yet Graham Dorrans, with his third goal in five days, and substitute Chris Wood both struck within the space of five minutes in the closing stages to inflict Huddersfield's first home defeat of the season.
The Baggies, who also hit a post through Marek Cech, may have avoided a third-round exit for the fifth time in the last six seasons but both sides would definitely argue promotion from their respective divisions is the bigger prize this season.
Roberto Di Matteo, twice an FA Cup winner with Chelsea, made five changes to the Albion side that beat Scunthorpe 3-1 on Monday to preserve second place in the Championship, although it is fair to say only two of those were due to rotation.
Counterpart Lee Clark was able to welcome Michael Collins back into the middle of midfield in what was the only change to the Town XI that edged out MK Dons 1-0 to keep them firmly in the League One promotion picture.
It was Dorrans who should have handed Albion the lead after 14 minutes when he met Chris Brunt's cross from just six yards out but the Scotland international could only volley over the bar.
The visitors were edging possession in the opening quarter although Town were making a competitive game of it, but maybe showing a bit too much respect to their second-tier opponents.
Brunt fired over the bar from 20 yards just before the half-hour mark after some well-worked build-up play but the Terriers, in contrast, were giving the ball away far too regularly.
Winger Brunt, who was at the centre of most things in the first half, forced a parried save from Alex Smithies as Albion continued to emphasise the difference in quality and composure.
But the strike proved to be the only effort on target during an opening 45 minutes in which an underperforming Town side hardly threatened.
Yet the home side started the second half in a much more positive manner, with Antony Kay heading Anthony Pilkington's cross wide after just 59 seconds.
But the Baggies soon proved their class again as Slovakia international Cech turned on the edge of the area and fired a left-footed effort against a post.
Huddersfield themselves enjoyed their closest chance just a minute later as Collins' run found Jordan Rhodes, he squared for Gary Roberts but the midfielder could only fire at Scott Carson from about eight yards out.
The Terriers again went close in the 64th minute as Collins lashed an effort narrowly wide with the tie finely balanced as the encounter entered the final 20 minutes.
Roberts again struck to force a routine save from Carson as the hosts started to pose more of a threat but it was Albion who then broke the deadlock with a sucker punch on the break.
Town gave the ball away on the edge of Albion's area and the visitors broke in numbers, outnumbering the home defence.
Youssouf Mulumbu found Dorrans and he coolly slotted home from 12 yards.
The clash was then put beyond any doubt in the 82nd minute as New Zealand international Wood converted a second from the middle of the area following another assist by Mulumbu.