Huddersfield 0 Albion 2
Graham Dorrans and Chris Wood booked Albion's place in the fourth round of the FA Cup with late breakaway goals to settle a drab game at the Galpharm Stadium.
Dorrans made up for missing a first half sitter after bursting away to break the deadlock with 13 minutes to go.
Chris Brunt, who had fed Dorrans for the opener, claimed another assist picking out substitute Wood for an 82nd minute strike.
But for long spells a flat Albion had looked destined to face a replay against their spirited League One hosts.
Temperatures began to plummet as the sun disappeared during the first-half and there was little on the field to warm the spectators.
Albion had more of the ball but they were sloppy in possession and consequently struggled to fashion genuine chances.
In-form home striker Jordan Rhodes had the game's first opportunity but screwed a far-post shot wide after Lee Novak's flick-on.
Dorrans' miss was the half's most memorable incident, as the Scot escaped his marker to beat the offside trap and arrive at the far post to meet Chris Brunt's cross, only to lift his shot over the bar from a couple of yards.
Brunt tried his luck twice from distance after cutting in from the right, but his first effort went over and his second was saved by goalkeeper Alex Smithies.
The second-half began in a similar vein to the first, but a chance eventually came at either end before the hour mark. Marek Cech hit the post for the Baggies with an excellent volley after a cross by Brunt.
Albion goalkeeper Scott Carson had to make a brave block to deny Gary Roberts, after the attacker found himself unmarked at the far post.
Moments later Michael Collins sent a shot wide from an excellent chance, after a left-wing cross and a lay-off from Anthony Pilkington.
But the breakthrough finally came on 77 minutes, as the Baggies broke from a Huddersfield corner through substitute Robert Koren.
The replacement found Brunt who delayed a pass perfectly to find the path of Dorrans, where the midfielder continued his lung-busting run and kept his composure to finish past Smithies.
It was 2-0 five minutes later, as Brunt beat the offside trap to meet Brunt's through-ball before completing a cool finish.