The young Reds scored the first and last goals of an entertaining game at Gillford Park but finished second best in this Conway Cup tie.
They had opened the scoring with a seventh minute goal from Josh Palmer who continued his bright start to the season with a close-range finish following a Hayden Percival corner.
But City bounced back and raced into a 4-1 interval lead, thanks to goals from Alex Cairns, Kieran Blair, Thomas Hickey and Bobby Dixon, although Reds were unhappy about a debatable penalty which gave the hosts their third.
Luck was also against them when a Jack Brown effort was cleared off the line when the scores were level.
It was still end-to-end stuff in the second half and Scott Paden-Gale made three important saves to keep City at bay.
There was only one goal in the second period, though, and it was a stunning effort from Reds’ Jack Dunstan (inset), his first for the club, ten minutes from time.
Team: Scott Paden-Gale, Ben Wade (Aaron Williams), Hayden Percival, Robbie Wilson (Owen Birkett), Zach Martin, Lewis Moore, Zach Lester (Hayden Rae), Cain Pears (Jack Dunstan), Josh Palmer (Milo Cooke), Jack Brown, Louis Webster. Substitutes – All used.