It took the Baggies just one minute to take the lead when Morgan Amalfitano's cross was punched straight into the path of Matej Vydra by Hugo Lloris, and the striker volleyed home into the bottom corner.
Tottenham had the chance to get a goal back when Danny Rose was brought down in the area and a penalty was awarded. However, Emmanuel Adebayor's spot kick was poor and saved by Ben Foster.
Pepe Mel's side extended their lead in the 31st minute when Sessegnon latched onto a ball over the top of the Spurs defence and slotted an effort past Lloris after outpacing Vlad Chiriches.
However, Tottenham were handed a way back into the game when Harry Kane raided down the right and lifted a cross into the area, and his ball in was deflected over Foster into his own net by Jonas Olsson.