Arsenal went ahead on five minutes from Dragomir’s header and could have had a second but Nketiah missed a penalty after being fouled.
Their lead was doubled when Dragomir, an 18-year-old Romanian midfielder, pictured above, finished off Joe Willock's through-ball 11 minutes before half-time.
Nketiah, less than 24 hours after playing in the UEFA Europa League defeat by Koln, confirmed the three points that lifted Arsenal above their opponents into fourth.
Arsenal: 30 Nov v Reading (H) PL Int Cup
West Ham: 11 Dec v Spurs (H) PL2