Shami bowled the fifth ball of the first over to Finn Allen at a venue that was making his international debut.
Mohammed Siraj sent Henry Nicholls caught in the slips for two, before Shami and Pandya took two catches and bowled to bowl out the visitors, whose skipper Tom Latham fell for one.
Phillips and Bracewell attempted to rebuild and brought back a 41-run sixth-wicket stand before Shami broke down.
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