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The son of former Priestfield favourite Barry Ashby opened the scoring as Gillingham were knocked out of the Papa John’s Trophy.
Harrison Ashby scored a neat opener at the Rainham End and Thierry Nevers added a second to settle the Southern Section Group A clash.
Gills boss Steve Evans named a strong side to take on the Hammers youngsters, knowing a win would see them through to the knockout stages of the competition.
The Gills had an early half-chance with Olly Lee’s left-wing cross evading first Charlie Kelman and then Vadaine Oliver at the back post.
Generally, though, West Ham looked comfortable and carried good threats out wide when getting forward.
The visitors scored two decent first-half goals and never looked like surrendering their advantage as Gills huffed and puffed.
West Ham’s opener came in the 23rd minute with Dan Chesters pulling the ball back to Ashby, who sidefooted home.
Kelman sent Hammers captain Aji Alese flying into the sponsor boards - making a fair old whack but causing no damage - before the Gills fell two behind in the 33rd minute.
The bright Nevers was the scorer, collecting a defence-splitting pass through the middle before rounding Aaron Chapman and slotting home.
Ashby continued to impress down the right early in the second half, setting up a chance for Keenan Appiah-Forson, whose strike was parried by Chapman, then Alese fluffed a header from a corner from six yards.
Gills went close to pulling a goal back when substitute Mustapha Carayol got down the left, broke into the box and forced a decent save from Krisztian Hegyi.
West Ham, meanwhile, should have added number three when Armstong Oko-Flex went on a great run but the finish didn’t match, blazing into the Brian Moore Stand.
Gillingham: Chapman, Jackson (McKenzie 55mins), Tucker, Kelman (Sithole 46mins), Lee, Reeves, Adshead, Lloyd (Carayol 66mins), Bennett, Oliver, Akehurst. Subs not used: Cumming, O’Keefe, Lintott.
West Ham: Hegyi, Nevers (Simon-Swyer 76mins), Oko-Flex, Alese, Ekwah, Ashby, Chesters, Longelo, Appiah-Forson, Potts, Baptiste. Subs not used: Kinnear, Dju, Rosa, Diallo, Laing, Greenidge.
Attendance: Not given.
Referee: Craig Hicks