The Baggies got off the mark quickly after Charlie Austin fired home the opener on his birthday, but the Tigers mounted a comeback to equalise.
The Baggies went 2-1 up before half time, courtesy of Ahmed Hegazi's header.
Hull once again levelled immediately after the break, only for Kamil Grosicki to respond almost immediately.
Grady Diangana tied up the points, whilst Matheus Pereira's performance was also impressive.
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