In their final home game of the season, Hammers claimed all three points thanks to Daryl McMahon's superbly taken free-kick in the 52nd minute.
The win made it five games unbeaten for Roger Cross' side and sets up a likely fifth placed finish with two more games to play, at Watford and Arsenal.
Once again, Hammers fielded a relatively inexperienced line-up for the visit of the Dons. Irish defender Clive Delaney was the oldest player in the team, at 23, while only Shaun Byrne and Stephen Bywater had tasted first team action.
Wimbledon also named a young side and there was an understandable sense of nervousness and caution among both teams in a first half that produced very little in the way of attacking quality.
Hammers did create one glorious chance in the 37th minute, when Byrne's neat pass released Greg Pearson, but the young striker fired his effort over the bar as Dons keeper Berni committed himself.
At the other end, central defenders Delaney and Elliott Ward dealt comfortably with the traditionally direct approach of the visitors, and Hammers went into the break looking a more confident and assured side.
Seven minutes into the second half, they made the vital breakthrough. After Byrne had been fouled some 25 yards out, McMahon stepped up to curl a direct free-kick over the wall and into the top corner of the net past the despairing dive of Berni.
Hammers' celebrations were delayed briefly as the Wimbledon players questioned the referee's actions in blowing his whistle just as the Irish midfielder made contact with the ball - presumably for encroachment by a member of the wall - but the official waved away the claims having played the correct advantage.
The visitors missed an excellent chance to equalise just five minutes later, when defender Herzig somehow headed wide from just six yards out, but that was the nearest the south Londoners came to testing Bywater.
Hammers occasionally threatened to double their lead, with left winger Mitchell Cole delivering a couple of teasing crosses that were cut out, while captain Byrne sadly wasn't rewarded for his tireless forward running from midfield.
The final whistle capped off a satisfying evening and a solid home record for the reserves this season that has provided four wins, eight draws and just one defeat from 13 matches.
Team: Bywater, A Ferdinand, Delaney, Ward, Tattam, McClenahan, Byrne, McMahon, M Cole, Pearson, Akinsete. Subs unused: Lumsden, Jackson, Wright, Laws, Blewitt, Bunce.