Austria international Arnautovic, who has been heavily linked with a big-money move to China, was left out of the Hammers' squad for the trip to the Vitality Stadium. Bournemouth top scorer Wilson has himself been subject to January transfer rumors and he returned from a two-game injury absence in style by smashing home early in the second half before Joshua King sealed a 2-0 win in stoppage time.
Wilson's powerful strike was his 10th Premier League goal of the season and is likely to fuel further speculation of him moving to Chelsea or replacing Arnautovic at the London Stadium. It also helped to end Bournemouth's five-match winless run in all competitions and secure just a third victory from its last 13 top-flight games.
Andy Carroll took Arnautovic's place in the only change made by Pellegrini following last weekend's win over Arsenal. With the game still goalless, Carroll blazed wildly over from around two yards out after Michail Antonio made a mess of the first opportunity.
Bournemouth perhaps had cause for complaint in the midtable clash when Nathan Ake's header was ruled out with 20 minutes played. Ake was onside when he headed home Ryan Fraser's inswinging cross from the left but assistant referee Adrian Holmes raised his flag, presumably against Wilson who challenged for the ball without touching it.
Bournemouth boss Eddie Howe opted to drop goalkeeper Asmir Begovic for the first time in the top flight since his 2017 move from Chelsea, preferring 38-year-old Artur Boruc.
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