The visitors managed to add two more goals late on, in the space of five minutes, to secure all three points. Kian Breckin scored from ragne after a quickly taken free-kick, whilst Bobb managed to net from close range.
The result means that the Under-21s remain in third place in the Premier League 2 Division 1 - five points behind Man City, who are now the league leaders, and three points off Chelsea in second place.
Crystal Palace: Whitworth, Kporha (Cadogan, 81), Grehan, Balmer, Adaramola, Rodney, Wells-Morrison, Ozoh, Omilabu, Akinwale, Mooney (Raymond, 75)
Subs not used: Izquierdo, Watson, Vigor
Manchester City: Van Sas, Samuel, Burns, Katongo, Galvez, Charles, Breckin (Agyemang, 84), Robertson (Adam, 75), Bobb, Mebude, Borges (Dickson, 81)
Sub not used: McNamara