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The forward struck twice in the first half, with Colin Rosler and Eric Garcia also on target for Gareth Taylor's men.
It was Manchester United who registered first, as Tahith Chong met Nishan Burkart's cross for an easy tap in at the back post, but Simmonds restored parity immediately after good work from Henry Ogunby.
Relatives of two former Blues, Tommy Doyle and Rosler combined for the second goal as the latter powered home a header to give City the lead.
United were well in the game and had the opportunity to equalise after Jeremie Frimpong fouled Chong in the area, but skipper, Angel Gomes, blazed his spot kick over the bar.
City capitalised and made the opposition pay for their profligacy, with Simmonds weaving in from the left to send a low effort into the bottom corner.
Garcia confirmed the victory as he met Ian Carlo Poveda's cross with a glancing header into the top corner.