Dorrans - who is reportedly being courted by a host of Premier League clubs ahead of a potential move before the end of the January transfer window - netted the first in the 78th minute.
And New Zealand international Chris Wood, fresh from signing a new deal with Albion last week, put the game beyond doubt four minutes later.
Huddersfield have the best home record in the country and initially it was hard to determine which team was second in the Championship and which was from League One.
But as the first-half progressed, five-time cup winners Albion became increasingly dominant and it was they who had the better chances.
Dorrans had an glorious chance, but when Chris Brunt's cross fell to him unmarked and two yards out all he could do was scoop it over the bar.
The quality of the play made neither side look worthy of their lofty league position, with Brunt the stand-out attacking player on the pitch and he went close with two long-range shots.
After the break the game opened up with the Terriers at last forcing Scott Carson to make a save, diving at the feet of Gary Roberts.
Marek Cech hit the post for the Baggies with a swivelling volley from the edge of box.
Both sides, meeting for the first time in the FA Cup since a 1929 quarter-final, pushed forward eager to avoid a replay.
And it cost Huddersfield dearly as, with the defence absent, Dorrans was released by Brunt and the Scotland international steered home his eighth goal of the season.
West Brom are undefeated after scoring first this season and Brunt created another goal within five minutes, this time putting Woods through on goal and the substitute did the rest.
Antony Kay came closest for Huddersfield with two minutes left but Carson saved well.