Chelsea took the lead in the 10th minute of the fixture, however, before Hazard - brother of first-team star Eden Hazard - made it 2-0 early in the second period.
James sent Chelsea three goals ahead on the hour with a calm finish, but the visitors were not done and added a fourth in the 78th minute through St Clair after good work from Joshua Grant.
United Under-23s have not won in the league since they beat Sunderland Under-23s at the end of October.
UNITED U23s (4-2-3-1): O'Hara; Riley, Olosunde, R. Williams, Borthwick-Jackson; Redmond, Hamilton; Dearnley, Gomes, Chong; Bohui
CHELSEA U23s (4-4-2): Cumming; Nartey, Grant, James, Sammutt; St Clair, McCormack, Christie-Davies (Colkett 59'), Castillo (Colley 75'); Hazard (Dasilva 62'), Redan