Daryl McMahon's double strike gave earned three points for the older boys, while a second half header from Tony Stokes earned a point for Kevin Keen's young side.
After successive 1-0 defeats in their last two matches, Tony Carr's team faced their London rivals just three days before Tuesday's FA Youth Cup quarter-final against Manchester City, but showed plenty of determination and ran out comfortable winners in the end.
After the Addicks had enjoyed the better of the opening exchanges, Hammers took the lead in the 25th minute when McMahon collected the ball on the left and cut inside before firing in a low shot that took a nasty bounce to deceive the goalkeeper and nestle in the bottom corner.
McMahon's second arrived 15 minutes into the second half, after Trent McClenahan had raced down the right and found Greg Pearson, who crossed low for the Irish midfielder to side-foot the ball home.
Charlton rallied in the closing stages but Hammers were well in control and kept the ball well to hold on for a morale-boosting victory ahead of Tuesday night's visit to the ground of non-league Hyde United for their cup clash with City.
Said Tony Carr afterwards: "We played a lot better today than we have done recently and thoroughly deserved the victory.
"With one eye on Tuesday night, I rested a couple who have played a lot of football lately, so we had a few younger lads in there and they responded well. We had no injuries and the performance was good, so it gives us a bit of a lift going into the cup game."
Team: Sealey, Laws, Tattum, Parrington, Blewitt, McClenahan, Bunce, Carrick, McMahon, Mehmet, Pearson (Cole 84). Subs unused: Jackson, Ferdinand, Akinsete, Lumsden.
Meanwhile, the a young under-17 side did extremely well to come from behind and snatch a point at Aston Villa.
With many regular players stepping up to the under-19s, Kevin Keen named no fewer than NINE schoolboys in his starting line-up, against a club renowned for their excellent youth set-up in recent seasons.
Villa took the lead halfway through the first half when a deep free-kick from wide on the right wasn't cleared properly and the loose ball was blasted home, but Hammers enjoyed their fair share of possession before the break and came out for the second half in determined fashion with a couple of new faces in the side.
Two more schoolboys, Brady and Stokes, came on for San Lee and Sos Yao respectively, and it was Stokes who made the vital contribution with 15 minutes remaining when he met Chris Cohen's cross with a header from the edge of the penalty area that squeezed into the corner of the net.
The kids might have snatched the win in the closing stages but had to make do with a deserved point that left Kevin Keen delighted with his team's performance.
"We played very well in the second half," he said, "and deserved our equaliser.
"I would say a point was a fair result. Villa just edged it in the first half, but we were the better side after half-time and, considering we played the whole half with ten schoolboys, I am very proud of their performance."
Team: Reed, Henry, Norval, White, Wright, Cohen, Noble, Shaw, Ephrain, Yao (Stokes 45), Lee (Brady 45). Subs unused: Welsh, Reid, Behcet.