Table-toppers extended their outstanding unbeaten run with a decisive 3-1 scoreline against a player-down their opponents.
Frank Lampard's team began to a flying start with their striker and Jamie Allen netting the goal within the initial minutes.
The Japanese winger added a 3-0 advantage just before the interval, while James Abankwah was sent off before the half.
The midfielder netted a spot-kick for the away side, but it turned out to be nothing more than a consolation effort.
Their keeper Carl Rushworth had previously blocked a one-on-one chance for Watford, which could have swung the match early on.
Lampard stated: “This was a challenging game this afternoon because the opposition are a quality outfit.”
The substitute came off the substitutes to net the only goal in a one-nil success over West Brom.
They controlled the game but only secured the tie late thanks to Clarke's fifth goal of the season.
West Brom thought they had netted in added time, but the goal was ruled out for a offense in the area.
The home player turned a late own strike to present Stoke a 1-0 result.
The home side have at present secured just a single match since the end of the summer.
The Stoke manager remarked: “This was one of the most important wins we’ve achieved this season.”
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