The Baggies will head into Saturday’s contest on a club-record run of 21 games without a win, while boss Alan Pardew has only collected four draws from his eight matches since taking over the reins.
Indeed, Albion are only off the bottom of the Premier League standings on goal difference alone, so the cup could act as a welcome distraction, particularly as they have not lost an FA Cup tie to a team from the fourth tier or below as a top-flight club in over 80 years.
Pardew has promised to pick a strong line-up against Exeter, although defender Craig Dawson and winger Matt Phillips will definitely miss the match due to fatigue and a hamstring problem respectively.
Exeter currently sit seventh in League Two and they are particularly impressive on home soil, as they have won their last four league games on their own patch.
The Grecians beat Heybridge Swifts and Forest Green to reach the third round for the second time in three seasons, following on from 2016 when they took Liverpool to a replay before losing 3-0 at Anfield.
Top scorer Jayden Stockley is a doubt for the match after breaking his nose against Newport last time out, while skipper Jordan Moore-Taylor missed that game with a muscle issue.
Defence could be a concern for Paul Tisdale’s side as Troy Archibald-Henville, Troy Brown and Luke Croll are all major doubts for the contest.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.