The under-17s secured their triumph over the Hornets thanks to a Greg Pearson free-kick on 29 minutes after Craig Saunders had been brought down just outside the area.
The Hammers deserved their half-time lead, with goalkeeper George Sealey rarely called into action and both Pearson and Saunders going close.
Minutes after taking the lead, Peter Brabrook's nearly added a second when a Saunders cross just eluded Daniel Morris at the near post. Ronnie Fletcher had the last clear chance of the half with a run from his own half into the opponents' area, but the keeper held his low shot.
In the second half, Hammers continued to attack the visitors, with both Saunders and Pearson once again the chief tormentors. In the final minute Pearson looked to have earned a penalty after being brought down in the area but the referee waved played on.
The midfield trio of Saunders, Tucker and Collington were impressive throughout, and captain Fletcher was strong in the tackle and inspired his younger team-mates to victory.
Meanwhile, Tony Carr's under-19s continued their impressive run of form with a single goal win over their Hertfordshire rivals at London Colney.
Darryl McMahon's strike secured the first league double of the season following a 3-1 victory over the Hornets back in November.
Louis Riddle made a welcome return as a second half substitute for his first competitive game since breaking his leg in the final reserve game of last season against Charlton
The under-19s have now won their last six matches and sit second in Group B behind leaders Ipswich.
Under-17s team: Sealey, Wright, Bunce, Parrington (Laws 85), Fletcher, Blewitt, Tucker, Collington, Morris (Noble 54), Pearson, Saunders (Lee 60). Subs Unused: Matt Reed, Chris Cohen.
Under-19s team: Jackson, Khan, Lumsden, Ward, Ferdinand, Carrick, Akinsete, Britton, Allen, Eastwood, McMahon. Subs: Niall Ritchie, Kes Metitri, Dean Cleaver, Louis Riddle