The hosts led when an incisive counter-attack saw Nugent race on to a glorious first-time Gelson Fernandes pass and slot home past keeper Frank Fielding.
Everton were penned back at the start of the second half, and Eriksson made a bold substitution after 54 minutes, sending on Rolando Bianchi and Gelson Fernandes for Nery Castillo and Didi Hamman.
The need for City to add to the squad in January has been underlined ahead of the trip to Hull City on Sunday, with Richard Dunne, Gelson Fernandes and Michael Johnson joining the list of absentees, though Vincent Kompany should be fit to return to action.