Abu-Bakarr Kargbo rounded Johnstone to find the net on 51 minutes while Jordan Richardson and Diego Arismendi spurned two chances in quick succession.
A rare opening for United was wasted when King headed straight at Nash after Wootton galloped down the right and delivered an inviting cross and Larnell Cole hammered a speculative effort well over the top. Wootton continued to enjoy moving forward and could not convert a difficult aerial opportunity after Fletcher dug out a cross from the right.
The Reds held out pretty comfortably in the end to start the campaign with a hard-fought victory and Fletcher will be delighted to get 90 minutes under his belt.
United: Johnstone; M.Keane, Thorpe, Wootton, Blackett; Cole, Fletcher, Tunnicliffe, Petrucci (Fornasier 69), Lingard (Veseli 91); King (Lawrence 90). Subs not used: Gollini, Januzaj.