A late penalty saw West Ham U21 claim the three points in Town's opening game of the Papa John's Trophy.
Paul Cook made 10 changes to the side who faced Bolton on Saturday, Kane Vincent-Young retaining his place in the starting XI.
Sam Morsy captained the side on his debut for the Club while 17-year-old Albie Armin also made his Blues bow in the middle of the defence.
Town got off to the perfect start as they took the lead inside three minutes. Vincent-Young pulled the ball back to Tom Carroll, who dinked a cross into the box. Norwood's initial headed effort was saved but the striker was on hand to poke the rebound into the back of the net.
The young Hammers levelled the match less than 10 minutes later, however, as Keenan Appiah-Forson's low shot from the middle of the box was too powerful for the outstretched arm of Tomas Holy.
Both sides looked dangerous on the counter attack, a cross fizzing across Town's six-yard box while Kayden Jackson fired over at the second time of asking from outside of the area after his initial effort had cannoned off of the legs of Idris El Mizouni.
Holy parried away Kamarai Swyer's near-post effort with just over half an hour played, the visitors once again turning defence into attack at speed.
Norwood and Jackson combined five minutes later but the latter's drilled cross was out of the reach of both Town's number 10 and Louie Barry at the back post.
The Blues saw penalty appeals waved away 10 minutes after the restart, referee Charles Breakspear adjudging Jamal Baptiste's challenge on Barry inside the box to be fair.
Cook was forced into his first change a few moments later as Jackson was unable to continue after a hefty tackle by Pierre Ekwah, the Hammers full-back receiving a yellow card.
Town continued to control the majority of the game, Matt Penney firing wide from 25 yards at the end of a driving run forwards.
The game sprung into life in a crazy 45 second period with just over 10 minutes remaining. First, Holy scrambled to claim a spilled free-kick before it could cross the line inside a packed penalty area. The Czech 'keeper released substitute Conor Chaplin with a long throw, the latter playing the ball inside to Zanda Siziba, who saw penalty appeals waved away after going down under a challenge from two West Ham defenders.
West Ham snatched the win late on, Armstrong Okoflex converting from the penalty spot after Holy had been adjudged to have fouled Baptiste.
The visitors' Amadou Diallo was sent off for a second yellow card in stoppage time.
Town: Holy, Vincent-Young, Woolfenden, Armin, Penney, Morsy (C), Carroll, Jackson (Chaplin 57), El Mizouni (Pigott 78), Barry (Siziba 66), Norwood.
Subs: Hladky, Baggott, Humphreys, Nolan.
Booked: El Mizouni, Morsy, Holy.
West Ham U21: Hegyi, Okoflex, Alese (C), Ekwah, Ashby, Chesters (Rosa 88), Laing, Longelo, Swyer (Perkins 70), Appiah-Forson, Baptise.
Subs: Kinnear, Dju, Diallo, Forbes, Casey.
Booked: Alese, Okoflex, Ekwah, Diallo (2).
Sent off: Diallo.
