Rice, who turns 20 on Monday, lashed home early in the second half to leave Arsenal without an away league success since Bournemouth last November.
The future of the London-born defensive talent is already assured, having recently signed a five-and-a-half year contract extension. His international destination is less certain - he is eligible for either England or the Republic of Ireland - but this was another step on the way to wider recognition.
West Ham have already rebuffed a £35 million offer from the Chinese but after Arnautovic's brother presented an impassioned case for the move to go ahead, the saga threatens to overshadow the forthcoming weeks.
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