The veteran midfielder fired home from the spot in the 86th minute after Richard Garcia had been denied a clear goalscoring opportunity by Addicks keeper Paul Rachubka - who was subsequently sent off for the offence.
It was the least Roger Cross's young team deserved for an impressive performance against an experienced Charlton side, who included the likes of Luke Young, Tahar El Khalej, Chris-Bart Williams, John Robinson, Jesper Blomqvist and Mattias Svensson in their starting line-up.
Despite taking a first half lead, the visitors' goal was their only effort on target in the entire 90 minutes and, while Hammers can't claim to have dominated throughout, they certainly showed more enthusiasm in attack and would have secured victory if young defender Elliott Ward had not missed the first penalty of the night on the stroke of half-time.
The hosts made the livelier start and, after Daryl McMahon had gone close with an attempted chip in the opening moments, should have taken the lead in the 12th minute, when Garcia collected a neat lay-off from Greg Pearson and burst clear of the Addicks defence. However, the Australian forward fired his left-foot shot inches wide of the post.
That early scare sparked some life into the visitors, but it was still a surprise when they took the lead in the 26th minute with their first and only notable attack of the game.
Former England under-21 defender Luke Young raced down the right and clipped over an inviting cross that was headed past Raimond Van der Gouw by skipper Michael Turner from six yards out.
A minute later, the hosts almost snatched an immediate equaliser, when the impressive David Noble's free-kick from 20 yards out was tipped over by Rachubka, but that was the closest either side came until the final minute of the half, when Hammers were handed a glorious opportunity to draw level.
McMahon's clever reverse pass released Pearson in the area, and the young striker was tripped by the Charlton keeper as he touched the ball on, leaving referee Appleby with no alternative but to point to the spot.
Ward stepped forward to take the kick but sadly couldn't repeat his success from 12 yards in the FA Youth Cup victory over Norwich City last week, as Rachubka dived to his right and palmed the effort wide.
The second half continued in similar fashion to the first, with both sides competing well in midfield and snapping in the tackle, but it was only Hammers who looked capable of finding the net.
Noble fired over the bar from 20 yards out in the 50th minute, while McMahon saw his over-hit free-kick from the right tipped on to the bar by Rachubka. With 16 minutes remaining, Garcia's superb effort from an acute angle was saved again, then Ward headed on to the top of the net, and Hammers could be forgiven for beginning to think it wasn't going to be their night.
With just five minutes remaining, though, substitute Danny Morris turned cleverly and fed a delightful ball through for Garcia, who bravely sandwiched himself between Rachubka and a defender to touch the ball goalwards before being clattered by the Charlton keeper.
The referee once again pointed to the spot, and this time applied the letter of the law to brandish the red card at the former Manchester United trainee.
Ward strode forward from the halfway line - gallantly indicating that he was prepared to make up for his earlier miss - but Moncur placed the ball down and fired the ball high into the net past substitute keeper Robert Elliot to ensure that the second string remain unbeaten at home this season.
Hammers: Van der Gouw, Schemmel, Minto, Ferdinand, Ward, Byrne,
Noble, Moncur, McMahon, Garcia, Pearson (Morris). Subs unused:
Forde, Blewitt, Lumsden, Carrick, Tattam.
Charlton: Rachubka, Young (Deane), Turner, El Khalej, Robson,
Robinson (Elliot), McCafferty, Bart-Williams, Blomqvist (Dincer),
Svensson, Campbell-Ryce.