Vardy is two games away from matching Ruud van Nistelrooy's record set in 2003 and is the league's top scorer with 11 goals in 11 matches.Riyad Mahrez had already scored in the 57th and 64th minutes as the visitors remained unbeaten on the road. Vardy added a third in the 77th.
Salomon Rondon's second goal in two games put the Baggies ahead at The Hawthorns after half an hour but they missed the chance to record three successive wins for the first time since 2012.
Rickie Lambert scored his first goal for Albion from the penalty spot late on.
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