City were two down inside 12 mins but rescued the game when subs Billy Kee and Johnny Hayes scored in the 2nd half.
Mercury match report here.
City reserve-team boss Gerry Taggart told The Mercury: "It wasn't rocket science to make the changes we did at half-time but they did make a difference.
"You will never come to places like Hinckley and get away with things easily.
"In the second half we earned the right, in the first half we didn't."
Hinckley: Mackenzie (Jupp 61), Mace, Giddings, Gooding (Jackson 70), Collins (Lister 45), Green (Platnaeur 45), Hall, Dillon (Roberts 72), Webster (Haughton 61), Lorougnan, Cartwright (Lavery 61). Unused sub: Taylor.
City: Cisak, Milnes, Rowe-Turner, Verma (Hinks 57), Parkes, Bolger, Douglas (John 73), Wesolowski, C King (Kee 45), Sappleton (Yussuf 70), Porter (Hayes 45). Unused sub: Ambrusics.