Rangers, with just one league win to their name, almost got off to the perfect start with Paul Bignot firing over the bar.
However, Hyde hit the hosts on the break in the second minute lead when Dan Turner played through Chris Sharp who kept his composure to slide home the opener.
The Boro deserved their 22nd minute equaliser with Jack Sherratt firing home before the hosts continued to probe.
Straight after the break Hyde regained the lead with a wonder striker by Paddy Lane finding the top corner with his effort.
Rangers probed for a leveller and substitute Jed Davies put his effort just wide in search for an equaliser.
However, any hope ended in the 79th minute when Liam Tongue fired his free-kick into the net to seal the points.