Steve Brackenridge put the home side ahead, but Jevons struck twice in the second period of extra time to put City into the semi-finals with a 2-1 win.
The Reserves have now make it 9 wins in succession in all competitions - having been defeated just twice all season - and are currently top of Division One East.
City line-up: Musselwhite, Edwards, Holt, Burton, Chapman, Strong, Williams, Philpott, Donaldson, Jevons, Pete.