The 18-year-old followed up his own header from a free-kick by Palace defender Gary Borrowdale to smash the ball home from close range.
Fellow City youngster Lee Croft, currently on loan at Oldham, came close to doubling the lead 10 minutes later when put through by new West Brom signing Richard Chaplow, but the 19-year-old hit the ball straight at the advancing Russian keeper.
Another City Academy product, Bradley Wright-Phillips, came on at the start of the second half in place of Lee Croft, and like Onuoha, won his first cap at any level for England.
Charlton's Luke Sam sealed the win in the 78th minute by firing home after Chaplow's cross - just 20 seconds after coming on.