The Blues were ahead after 20 minutes when good work by Antoine Sibierski set up Wright-Phillips to finish neatly.
The young striker doubled the lead just before half-time from close-range as City dominated the play.
Robert Sissons pulled one back for the Trotters against the run of play, but Ishmael Miller's 57th minute penalty sealed the win on a freezing night at the Regional Athletics Arena.
TEAM:
Ashton, Powell, Stott, Whitehead, Hill, Fojut, Campo (Sissons 46), Fernandes, Jamieson, Sinclair (Thompson 74), Smith.
SUBS NOT USED:
Kazimerczak, Charlesworth, Buval.