While the senior team's result left boss Tony Carr delighted, the day was also a personal triumph for young striker Billy Mehmet, who returned to action after almost a year on the sidelines with a back injury, and scored the vital third goal within 10 minutes of appearing as a substitute.
Freddy Eastwood had given the Hammers a 25th minute lead when he took advantage of a goalmouth scamble and tucked the ball home, but the scores were level just 10 minutes later when some loose marking handed the Canaries an equaliser.
The lead was restored on the stroke of half-time when Anthony Dean's low free-kick took a ricochet off a defender and landed at the feet of Phil Lumsden, who fired in from close range.
Norwich fought bravely to stay in the game and brought a fantastic save out of Glenn Jackson early in the second half, but the tension was lifted in the 65th minute when Mehmet converted and Eastwood's second of the game a few minutes later rounded off an excellent team performance.
Said Tony Carr afterwards: "It was a tough game, and certainly not as easy as the score suggests. Norwich battled away and, until we scored the third, it was a very close affair.
"The big highlight of the day was Billy Mehmet's goal. It has been a tough year for Billy but he has worked hard to return and it was a real pleasure for everyone to see him come on and score.
"The result gets us back on the winning trail and we want to try and get that second place in the group. I don't think we can catch the leaders Ipswich, but finishing second would be a great achievement after the start to the season we had."
Team: Jackson, Khan, Lumsden, Ferdinand, Ward, Smith (Ritchie 70), Akinsete (Mehmet 55), Britton (Fletcher 72), Allen, Eastwood, Dean.
Meanwhile, Peter Brabrook's under-17 side were left frustrated by a determined Charlton team in a game the Hammers really should have won.
Despite dominating for most of the game and creating several goalscoring chances, the Hammers conceded first when goalkeeper George Sealey rushed out of his goal to make a clearance but misjudged the flight of the ball and lost possession, allowing the Charlton striker to tap into an empty net.
Greg Pearson and Liam Parrington both wasted good chances in front of goal before Mitchell Cole somehow headed over the bar from just a few yards out and, as the game wore on, it looked like ending in defeat for the Hammers.
However, with just a few minutes remaining, the Hammers finally made a deserved breakthrough when Pearson crossed for 14-year-old substitute Sose Yao to slot home.
A relieved Peter Brabrook said afterwards: "A point was the least we deserved after outplaying Charlton for most of the game. We played well and created lots of chances, but our luck just seemed to be out in front of goal.
"We became a little bit desperate after they scored and I threw a striker on for a midfielder to go with three up. It was really only a matter of time before we scored and it was nice for the young lad to pop up with the equaliser.
"Once again, I had a team of mostly schoolboys out there, and they did themselves proud. Charlton had seven or eight staff boys in their team, but we were the better side and deserved to win.
"There are some very good players coming through and, as long as they don't get carried away, we should have a good set-up next year."
Team: Sealey, Wright, Parrington, Laws, Blewitt, McClenahan, Collington (Morris 55), Tucker (Noble 20), Saunders (Yao 80), Cole, Pearson. Subs unused: Cohen, Read.