First-half goals from Salomon Rondon and Jonny Evans looked to have been enough to nullify Abdoulaye Doucoure's strike, but Richarlison's equaliser deep into added time meant that Marco Silva's men extended their run on the road.
Watford started the game in a fashion that their impressive away form might have indicated before the game, but they soon found themselves behind when a standout piece of finishing saw Rondon hold off his marker before lashing beyond Heurelho Gomes from an improbable angle.
SIlva's men were left to rue yet more costly errors at the back just minutes later, when Matt Phillips turned a corner towards the front post in the 21st minute, leaving Doucoure's poor clearance to find Evans at the back post, and he made no mistake with a simple header to earn his side a two-goal lead.
Watford continued to fight for a route back into the contest despite the deficit and they were rewarded for some impressive industry before the break, when Richarlison fed Doucoure down the left channel, allowing the midfielder to produce a standout finish down low beyond Ben Foster.
Richarlison's impact on the contest became increasingly prominent and he might have pulled things level just before the break, but the youngster saw his curling effort creep just wide of Foster's far post.
The 20-year-old continued to threaten early in the second period and his work almost saw Etienne Capoue profit from range, before seeing his driven effort miraculously deflected wide of the target by a retreating Gareth Barry.
With Watford's unbeaten away record facing an end, Silva threw on record signing Andre Gray for the remaining 15 minutes, but the frontman was unable to make his mark on the encounter thanks to some adroit West Brom defending.
It looked as though the Baggies would walk away with all three points, but a costly free kick deep into injury time proved vital, as Richarlison rose highest inside the area in order to send the ball beyond Foster and the visiting fans into a frenzy.